Constitutive Priors for Machine Intelligence: A Legitimacy Theory of the Artificial Physical World

Jiang Jiang; Yifu Sun; Qi Shen

cs.AIAug 15, 2026

Constitutive Priors for Machine Intelligence: A Legitimacy Theory of the Artificial Physical World

Authors: Jiang Jiang, Yifu Sun, Qi Shen

Organizations: Persagy Science and Technology Co., Beijing, China

Abstract

Machine intelligence's push into the physical world is stuck on a gap: deployment demands auditable judgments from day one, fault samples are scarce or absent, and the norms defining "what counts as a fault" live in design documents, not in operational data. We argue this gap is structural, and locate where it can be legitimately closed. We divide the worlds machine intelligence faces into four (phenomenal, basic physical, artificial physical, artificial symbolic) along one axis of constraint strength, and give the Promulgation Criterion: extracting a prior framework from a world is legitimate if and only if the world is intentionally constituted (C1) and has left a readable generative archive (C2). On the criterion's two gradient axes, exactly one world is high on both: the artificial physical world (buildings, factories, infrastructure), whose norms precede their instances; the legitimate path is to extract the framework from the archive, not to induce it from data. We then show what shape such a framework must take: four construction goals force four incompatible carriers, hence at least four layers (syntax, concepts, knowledge, instances); on a closed concept layer fault localization is decidable in polynomial time, and every judgment is interrogable, traceable to a promulgated clause. The same criterion fixes the runtime division of labor with LLMs: promulgatable duties go to rule engines, on-site judgments beyond promulgation go to LLMs, and every generation sandwiched by promulgated clauses is auditable. The theory is falsifiable: four bets (P1-P4) with explicit falsification conditions -- among them that the next large-scale AI breakthrough occurs in the artificial physical world. Evidence: formal proofs (Appendix A); two cases (Appendix B: a cooling plant; the Curiosity rover Sol 1536 anomaly); eight reverse-read lineages, from BACnet to RDF/OWL (Appendix C).

Figures & tables

This paper	The DL tradition
syntax layer	signature (vocabulary)
concept layer	TBox (terminological axioms)
knowledge layer	rule base (rule extensions)
instance layer	ABox, extended with streaming data

Table 1

Route	Data source	Direction of fit	Failure semantics	Zero-shot operable
Deep learning	instances	description	silent drift	no
World models	video, interaction	description (prediction)	silent	no
Large language models	human symbolic corpora	description	no promulgated clause to check against (hallucination)	"yes" within the symbolic domain
PINNs	observations + laws	description (explicit)	prediction error, not violation	no
Knowledge graphs	extracted concepts	description	none	partial
MBD/DX	system description (promulgated by the modeler)	promulgation (the promulgator is the modeler, not the world’s design archive)	conflict sets	yes

Table 2

World	Examples	Data interface	Constraint structure	Rule source
Phenomenal world	cold weather, soft cloth, a cool breeze	continuous high-dimensional sensory stream; no ready-made segmentation	weakest (open)	none
Basic physical world	pushing a box, tiring when lifting	obtained in interaction with nature	the laws themselves are highly compressible, but the behavior of composite systems is effectively open to the learner	none; laws are discovered descriptions, not promulgated rules
Artificial physical world	lamps, air conditioners, buildings, machines	dual channel: physical instances plus design archives	strong (dual constraint of physics and intention)	present (rules promulgated in design archives)
Artificial symbolic world	writing, books, programs	discrete symbols, written-to-be-read	strongest (closed)	split: code precedes its instances; language follows its instances (see Section 3.7)

Table 3

Goal	Provenance	Consequence of removal
Stability	S2 (promulgated constraint): promulgative authority must hold in both postures, type and clause	concept cores drift with data; "fault" loses its definition; the promulgation leg breaks on the spot
Openness	the world picture of Chapter 3: the object list and the observation stream keep growing	the framework is trapped in staleness: new artifacts, new operating conditions, new failure modes cannot enter; the service range stops at promulgation day
Abstraction	S2, posture one: constrain instances as types; experience accumulates across instances	degenerates into an all-instance record (i.e., posterior learning itself) and "prior" loses all meaning
Concreteness	S2, posture two: anchor instances as clauses; judgments must land on the ground	concepts talk to themselves and cannot anchor this chiller or this ward: concepts spin idle and never reach the field

Table 4

Merged cells	Shared discipline	Conflict
$(F,T)$ and $(I,T)$	$\delta=T$	$\rho$ : freeze vs intake
$(F,N)$ and $(I,N)$	$\delta=N$	$\rho$ : freeze vs intake
$(F,T)$ and $(F,N)$	$\rho=F$	$\delta$ : type vs instance
$(I,T)$ and $(I,N)$	$\rho=I$	$\delta$ : type vs instance
$(F,T)$ and $(I,N)$	none	both $\rho$ and $\delta$
$(I,T)$ and $(F,N)$	none	both $\rho$ and $\delta$

Table 5

Appendix figures & tables31 assets

Supplementary material from the paper’s appendix.

Appendix

Part of speech	Grammatical role
PhysicalObject	bearer of the physical world
CompositionRelationType	part–whole structure
MappingRelationType	cross-domain correspondence
AttributeType	structural bearer of composite attributes
FailureMode	the mode of action of a failure
TriggerFactor	exogenous disturbance source (can only be a cause, never an effect)

Appendix

Table 7

Connector	Grammatical function
hasAttribute	attaches a composite attribute structure
hasComponent	composition structure
manifestsAs	reasoning node $\to$ failure mode
relatesFrom / relatesTo	the two ends of a generic directed relation
hasFailureNode	model $\to$ its nodes
hasRelationFrom / hasRelationTo	head and tail of a causal edge

Appendix

Table 8

Part of speech	Concepts under it
PhysicalObject	equipment types, component types, medium-unit types, entity-combination types, space types, system types, tool types, instrument types, operation-consumable types, operation-spare-part types, protective-equipment types
FailureMode	physical-system failure mechanisms, medium-state failure mechanisms, system transfer factors, environmental factors
TriggerFactor	personnel-operation factors, rule-constraint factors
FailureReasoningNode	failure-hazard nodes, failure-inducement nodes, failure-consequence nodes
SystemReasoningElement	failure propagation channels, system-failure input nodes, in-system equipment-failure nodes, system-failure output nodes, system-failure state nodes
RiskEvent	space risk events, system risk events, equipment risk events

Appendix

Table 9

Depth	Scope	Node	Entity	Failure mode	Reduction category	Prior MTTF	Observation / maintenance plan
1	medium unit under equipment	HZ-P1	MDU-OIL lubricating oil	FM-MED-01 lubricant property degradation	physical-property degradation failure	17,520 h (Weibull)	manual low-frequency observation / periodic replacement
2	component under equipment	HZ-P2	CMP-BRG pump bearing	FM-PHY-01 bearing seizure	degradation & wear failure	43,800 h	IoT observation / replacement upon symptom observation
3	entity combination under equipment	HZ-P5	ECP-MECH mechanical transmission chain	FM-PHY-04 rotor mechanical jam	function interruption failure	52,560 h	—
4	the equipment under analysis	HZ-P0	ACCCCP chilled-water pump	FM-PHY-02 unable to supply water	function interruption failure	35,040 h (exponential)	IoT observation / repair after failure
leaf	exogenous inducement	TN-P2	—	HOF-01 outlet valve mistakenly closed	personnel-operation factor (TriggerFactor enumeration)	—	—

Appendix

Table 11

Entry	Type	Content
PC-HZ-P2	propagation condition	applicability whitelist (DNF): BUSINESS_SCENE / HIGH_COOLING_LOAD > 40%
PSRE-PC-HZ-P2-1/2	degree-level mapping	0.5 $\to$ 0.5 ; 1 $\to$ 1
HDS-P0-L50	graded state description	direct observation: "the chilled-water pump shows symptoms of declining water-supply capacity and is at risk of failure"; uploaded: "symptom state uploaded from subordinate nodes (bearing wear, seal leakage)"
HDS-P0-L100	graded state description	direct observation: "the chilled-water pump is unable to supply water"; uploaded: "failure state uploaded from subordinate nodes (rotor mechanical jam / electrical drive circuit function interrupted); the unit as a whole has lost water-supply capacity"

Appendix

Table 12

Link	Entry	Key content
information-point slots	DIP-P001 / P002 / P003	flow instantaneous flow (trigger point), inPress inlet pressure, runStatus running state; object class ACCCCP , source TWIN_DATA ; slots only — they contain no readings
external input	EPT-DESIGN-FLOW	ratedOutletFlow rated outlet flow, carried with the object class
reduction	SEE	trigger type THRESHOLD_CROSSING ; formula flow / ratedOutletFlow , dimensionless result
threshold	LTT-TR-1	THR_CWP_FLOW_LOW = 0.8 , direction DOWN_CROSSING , deadband 2%, duration 60 s
rule	JRI-RULE_FLOW_CRIT	condition 1 CTT-RULE_FLOW_CRIT-1 : P003 EQ RUNNING ; condition 2 CTT-RULE_FLOW_CRIT-2 : P001 LT 8 m 3 /h
conclusion	JC-FLOW_LOSS_CRITICAL	"supply flow approaching zero; the pump has lost water-supply capacity"; exclusion group G_FLOW

Appendix

Table 13

Entry	Type	Key content
CQ-P1	failure-consequence node (propagation edge)	failure mode STF-02 (transfer type = matter); scope: the system ACCC the equipment sits in
SIE-C2	in-system equipment-failure node	equipment class ACCCCP ; bridges to HZ-P0 via EFR-C2-1/2 ; gating PC-SIE-C2
SS-C1	system-failure state node	system class ACCC ; primary failure mode STF-04 ; two input rules SFR-C1-1/2
SO-C1	system state object	the runtime degree-level bearer of SS-C1 ; returning to zero means its degreeLevel returns to 0 ; records are append-only
RE-03	equipment risk event	anchored to HZ-P0 ; cascading failure, barrier = redundant switchover; loss structure binary model ; recovery path = redundant recovery
RE-02	system risk event	anchored to SS-C1 ; affects ACATAH , SPC-OFFICE ; loss structure linear amplification

Appendix

Table 14

Content	This case	The knowledge-layer slot it lands in
physical individual	chilled-water pump #1, data-center zone A	instantiates object class ACCCCP
time-series readings	flow , inPress , runStatus	DIP-P001 / P002 / P003
static parameter injection	ratedOutletFlow = 480 m 3 /h ; npshRequiredInletPressure = 85 kPa	EPT-DESIGN-FLOW / -NPSH-PRESS
runtime states	the degreeLevel of each hazard node	runtime fields of knowledge-layer nodes

Appendix

Table 15

Step	Time	Action	Inter-layer edge	Entries relied on	Result
1	08:06	readings land	L4 $\to$ L3 instantiation (slot filling)	DIP-P001 / P002 / P003	flow=462 , inPress=128 , runStatus=RUNNING assigned into the three slots by object class and point code
2	08:06	reduction	L4 $\to$ L3 instantiation (value $\to$ ratio)	SEE formula + EPT-DESIGN-FLOW	462 / 480 = 0.963
3	08:11 / 08:12	threshold crossing	within L3	LTT-TR-1 ( 0.8 , down-crossing, 60 s, 2%)	at 08:11 ratio 0.760 had crossed down but debounce was unmet ( not triggered ); at 08:12 ratio 0.646 sustained over 60 s: SEE triggered
4	08:14	rule adjudication	within L3	the two conditions of JRI-RULE_FLOW_CRIT	conclusion FLOW_LOSS_CRITICAL
5	08:14	degree-level write-back	L3 $\to$ L4 collapse landing	SOT-FLOW_LOSS_CRITICAL-1	HZ-P0.degreeLevel refreshed from 0 to 1 ; HDS-P0-L100 supplies the human-readable sentence; BMS level-1 alarm
6	08:14	model routing (three routes)	within L3 (cross-model)	ARNP-1	(1) enter equipment cause-tracing; (2) EFR-C2 bridges HZ-P0 $\leftrightarrow$ SIE-C2 ; (3) the cavitation branch RULE_CAVI not hit — HZ-P6 stays 0 with a "not activated" record

Appendix

Table 18

Rule	Condition	This time
RULE_FLOW_OK	flow/rated $\geq$ 0.9	no (0.006)
RULE_FLOW_DEG	RUNNING and 0.8 > flow/rated and flow $\geq$ 8	no ( flow < 8 )
RULE_FLOW_CRIT	RUNNING and flow < 8 m 3 /h	yes ( CTT-RULE_FLOW_CRIT-1 : P003 = RUNNING ; CTT-RULE_FLOW_CRIT-2 : 2.8 < 8 )

Appendix

Table 19

Causal edge	Path	Grounds for exclusion
CR-P7	TN-P2 (outlet valve mistakenly closed) $\to$ HZ-P0	valve-position feedback fully open; 07:30 patrol record shows normal valve position
CR-P8	TN-P3 (planned maintenance shutdown) $\to$ HZ-P0	no maintenance work order; P003 = RUNNING
CR-P14	IN-P4 (cooling-source water parameter anomaly) $\to$ HZ-P3	cooling-plant supply temperature normal; IN-P4.degreeLevel = 0

Appendix

Table 20

Norm	What if it were treated as a "physical discovery"
THR_CWP_FLOW_LOW = 0.8	no explanation of why different projects take different values
THR_CWP_FLOW_ZERO = 8 m 3 /h	physically there is no essential difference between 8 and 7.9
duration = 60 s , deadband = 2%	the physical process itself has no "60 seconds" boundary
ECP-MECH being one entity	no such thing can be disassembled out
the 32-category reduction basis	nature provides no classification
the four-grade state semantics	physical quantities are continuous

Appendix

Table 21

Interrogation	Entry the answer points to
by what right is the flow called abnormal?	SEE.measurementReductionFormula , input source EPT-DESIGN-FLOW
by what right is the threshold 0.8?	LTT-TR-1.thresholdDefault1 , overridable with a trace
by what right CRIT rather than DEG?	CTT-RULE_FLOW_CRIT-2 ( flow < 8 ) holds; RULE_FLOW_DEG requires flow $\geq$ 8 , which fails
by what right is HZ-P0 a 1 rather than a 0.5?	SOT-FLOW_LOSS_CRITICAL-1.targetDegreeLevel
what does this 1 mean to a human?	HDS-P0-L100.directObservationStateDescription
by what right was the mistakenly closed valve excluded?	the inducement end TN-P2 of CR-P7 was falsified by valve-position feedback and the patrol record

Appendix

Table 22

Phenomenon	Verdict	Grounds
reading out of bounds, rule hit	Violation(i)	L3 norms complete; L4 data non-compliant
reading finds no slot	CoverageGap	no matching object class + point code in L3
failure mechanism reduces to none of the 32 categories	CoverageGap	no matching value in the enumeration basis
two channels give different degree levels	MaintenanceFault	internal inconsistency of the knowledge layer (A1 failing)
no explanation after all paths excluded	CoverageGap	causal tree incomplete

Appendix

Table 23

Depth	hazardEntityScope	Node in this case
1	medium unit under equipment	HZ-P1 (lubricating oil)
2	component under equipment	HZ-P2 (pump bearing)
3	entity combination under equipment	HZ-P5 (mechanical transmission chain)
4	the equipment under analysis	HZ-P0 (chilled-water pump)

Appendix

Table 24

Layer	Scale	Change frequency	Direct human readability	Machine adjudication cost
L1	30 items	frozen	requires ontology training	extremely low (shape matching)
L2	107 classes + 32-value basis	only added, never altered	requires industry training	low (enumeration lookup)
L3	thousands of entries	frozen clause by clause	readable by domain experts	medium (graph traversal, bounded)
L4	unbounded stream	appended by the second	directly readable by operators	high (continuous quantities, need reduction)

Appendix

Table 25

Merger	Conflicting goals	Consequence on this case
L1 + L2	stability vs openness	every newly added failure mechanism would touch the syntax layer; the semantics of connectors like manifestsAs would loosen; HZ-P2 manifestsAs FM-PHY-01 would mean different things in different periods; all historical reasoning traces would fail
L1 + L3	abstraction vs concreteness	ACCCCP and 35040 would appear in the syntax vocabulary; switching industries would mean switching grammar; cross-domain reuse drops to zero
L1 + L4	stable $\wedge$ abstract vs open $\wedge$ concrete	the syntax would change with every reading — untenable
L2 + L3	openness vs stability	augmenting with new knowledge and modifying existing concepts become indistinguishable; the ModelDefect / Violation distinction vanishes; the 32-category basis gets casually expanded along with knowledge augmentation, and Proposition A.16’s upper bound fails
L2 + L4	abstraction vs concreteness	0.8 gets learned away by field data; promulgation degenerates into fitting; S2 vanishes
L3 + L4	stability vs openness	the write at 08:14 setting the degree level to 1 would rewrite HZ-P0 itself; priorMTTF = 35040 would be contaminated by one pump’s single failure; the 12:05 return to zero could not restore it; the audit trail is lost; C2 fails

Appendix

Table 26

Stage	Time	Content	Source
stall and autonomous termination	Sol 1536	encoder zero change, current at limit, stall determination, sequence termination	(Kinnett et al., 2022)
winding/harness exclusion	Sol 1536 telemetry	routine continuity checks plus voltage/current telemetry normal; motor windings and harness falsified	(Kinnett et al., 2022)
initial hypothesis set	2016-12	encoder electromechanical failure / motor assembly mechanical blockage / gearbox failure / brake release failure / control-system failure	(Kinnett et al., 2022); the "encoder/brake" two-candidate version in early public reports, see (NASA/JPL, 2016)
convergence on the brake	2016-12 to 2017-03	coils energized separately, current raised, both coils energized together, repeated attempts — behavior consistent $\to$ individual coil differences excluded, pointing to interference with the moving brake disk; working hypothesis: a displaced part or foreign object debris (FOD)	(Kinnett et al., 2022; Clark, 2016; Lakdawalla, 2017)
blockage signature	first half of 2017	diagnostics showed an intermittent high-resistance state recurring "once per revolution," worsening with use	(Kinnett et al., 2022; Vasavada, 2022)
commonality across same-type motors	Sol 1627 (2017-03)	the drill chuck motor (same model) showed a similar failure signature $\to$ a system-level common factor surfaced; the turret CHIMRA vibration mechanism was identified as the common stressor and its use was thereafter restricted	(Kinnett et al., 2022; Vasavada, 2022)

Appendix

Table 27

Depth (scope level)	Scope	Node	Entity	Failure mode	Reduction category	Historical correspondent
leaf	exogenous inducement	TN-FOD	—	foreign object debris intruding into the brake gap	foreign-object intrusion (environmental-factor basis, carried over)	the FOD working hypothesis (Kinnett et al., 2022; Clark, 2016)
leaf	exogenous inducement	TN-VIB	—	accumulated CHIMRA vibration stress	mechanical environment (environmental-factor basis, carried over)	the same-type-motor commonality, the accelerated degradation after Sol 1651 (Kinnett et al., 2022; Vasavada, 2022)
2	component under equipment	HZ-BRK	DRILL_BRAKE moving brake disk	brake not fully released	function interruption failure (carried over)	hit : the converged conclusion (Kinnett et al., 2022; Lakdawalla, 2017)
2	component under equipment	HZ-ENC	magnetic encoder	encoder electromechanical failure	function interruption failure (carried over)	excluded: encoder field counts varied normally during brake cycling (Kinnett et al., 2022; Lakdawalla, 2017)
2	component under equipment	HZ-MOT	feed motor assembly	motor assembly mechanical blockage	function interruption failure (carried over)	excluded: the "once per revolution" intermittent high-resistance signature localizes to the brake-disk interface rather than the motor interior (Kinnett et al., 2022; Vasavada, 2022)
2	component under equipment	HZ-GBX	transmission	gearbox failure	function interruption failure (carried over)	excluded: public sources record the exclusion conclusion but not the specific grounds (Kinnett et al., 2022)

Appendix

Table 28

Step	Time	Action	Inter-layer edge	History / reconstruction
1	Sol 1536	telemetry lands	L4 $\to$ L3 instantiation	history: encoder zero change, current at limit (Kinnett et al., 2022)
2	same	stall determination triggers	within L3	history: the onboard counterpart of LTT-STALL really triggered (Kinnett et al., 2022)
3	same	sequence termination + high-rate buffer dump	L3 $\to$ L4	history: the flight software terminated autonomously (Kinnett et al., 2022)
4	same	degree-level write-back HZ-FEED = 1 , alarm	L3 $\to$ L4 collapse	reconstruction (onboard there were only fault codes, no degree-level semantics)
5	same	route the cause-tracing model, enumerate the candidate set	within L3	reconstruction: the five candidates enumerated immediately — on the ground, assembling the same set actually took weeks (Kinnett et al., 2022)
6	the ensuing diagnostic period	exclusions: windings/harness (continuity checks), encoder (encoder field counts varied normally during brake cycling), control system (command chain normal elsewhere)	within L3	the excluded items and the grounds of exclusion are both taken from the historical record (Kinnett et al., 2022; Lakdawalla, 2017); the framework only makes the order and the adjudications explicit

Appendix

Table 29

Stage	The actual process	The in-framework replay
stall determination	onboard, immediate (promulgated rules already on duty)	the same (Steps 1–3 are history)
hypothesis-set assembly	a ground expert team, several weeks	the promulgated model enumerates immediately (Step 5)
order of exclusions and grounds of adjudication	improvised on the spot, written up after the fact (Kinnett et al., 2022)	the tree structure promulgated in advance; exclusion experiments checked against clauses
common-factor identification	chance discovery on Sol 1627	systematic hit of the gating condition (Step 8)
total diagnostic period	about 4 months to convergence, 521 sols to workaround recovery	enumeration-tree traversal + scheduling of the pre-set exclusion experiments
absorption of new operating modes	engineering rework (FED/FEST)	concept augmentation (port of entry); the framework unmoved

Appendix

Table 30

Layer	Counterpart	Promulgator
syntax	the application data-type system (Boolean/Unsigned/Real/Enumerated/Date/Time/ObjectIdentifier…) plus the "object–property–service" metamodel: everything in the world presents as an object, objects are described by properties, actions are initiated through services	ASHRAE SSPC-135
concepts	the closed set of standard object types : 18 types in 1995 $\to$ 54 in 2012 $\to$ 61 in ISO 16484-5:2017 (Analog Input, Schedule, Trend Log, Event Enrollment, …); enumerated property identifiers , over 160; closed enumerations of engineering units, reliability, event states, etc.	ASHRAE SSPC-135
knowledge	the five classes of service primitives (object access / device management / alarm & event / file transfer / virtual terminal); BIBB interoperability capability blocks + PICS conformance statements — a testable specification of "how a device shall respond"	ASHRAE SSPC-135
instances	object instances in concrete devices (addressed by type + 22-bit instance number) + Present_Value real-time values, directly grounded to sensors	deployment sites

Appendix

Table 31

Layer	Counterpart	Promulgator
syntax	the network-variable (NV) type system + the XIF device interface file format: a device self-declares in XIF "what I can say" (each NV’s name, direction, type)	Echelon/LonMark
concepts	the SNVT master list (resource files under continuous versioned expansion; the verified starting point is v7 = 114 types): each type promulgates dimension, resolution, legal range, the invalid value , scale factors, down to field-level bit definitions; SCPT configuration-parameter types; ENUM enumeration types	LonMark International
knowledge	Functional Profiles : each Profile promulgates the minimal NV set a functional node of a given kind shall expose, divided into mandatory and optional items (thermostats, pump controllers, valve positioners, …)	LonMark International
instances	bound NV instances in a commissioned network	deployment sites

Appendix

Table 32

Layer	OPC DA (1996)	OPC UA (1.0 released 2008; adopted into the IEC 62541 series in batches from 2010)
syntax	COM/DCOM interface shell (Windows only)	the address-space metamodel: nodes / references / type hierarchies / namespaces (IEC 62541-3)
concepts	$\times$ flat tag list, no type system	Companion Specifications : industry organizations promulgating closed sets of object types for their industries — OPC 40001 Machinery, OPC 40501 Machine Tools (umati), OPC 30050 PackML, EUROMAP 77 injection-molding machines (OPC 40077), etc., released successively in recent years
knowledge	$\times$	the four families of the base model: DataAccess / Alarms & Conditions (alarm logic = the promulgation of behavioral norms) / HistoricalAccess / Programs
instances	tag values	live nodes in the server’s address space

Appendix

Table 33

Layer	Status
syntax	✓PDU + function codes + four data-table classes
concepts	$\times$ register semantics drift into vendor PDFs: whether 40001 is a temperature or a pressure, the protocol itself does not say
knowledge	$\times$ none
instances	✓real-time register values

Appendix

Table 34

Layer	COIN counterpart	Character	Argument
syntax	the workflow signature + the monad composition laws (unit/bind and their laws)	stable $\times$ abstract	exists prior to all concrete tasks; prescribes "which constructs are composable and which laws composition must satisfy" — the office of the syntax layer
concepts	the type constraints of the typed task space (type declarations such as UserID, AuthResult)	open $\times$ abstract	type declarations prescribe which plans are legal (plan admissibility), not what the world happens to contain: normative assertions, not factual ones; the type library can be augmented as the task domain expands
knowledge	per-task generated, compositionally certified and finalized decomposition trees and compiled blueprints, together with their certificate chains	stable $\times$ concrete	a blueprint records "which combinations of local solutions have been verified to work": stable (unchanged after finalization) and concrete (anchored to a specific task)
instances	real-world instances land indirectly through leaf contracts + external implementations	open $\times$ concrete	COIN’s applicability gate (its §2.1: applicable only after the relevant context has been made explicit) itself acknowledges the indirectness of the instance layer: a pure calculus does not touch the world directly; the world’s access presupposes explicit contracts

Appendix

Table 35

Layer	Counterpart	Promulgator
syntax	RDF triples + tagset construction rules	W3C / the Brick community
concepts	the Brick class hierarchy and tagset controlled vocabulary; the Haystack tag vocabulary (a versioned vocabulary, only added, never altered)	the Brick community committee / Project Haystack
knowledge	SHACL validation rules: the shape constraints entities shall satisfy (e.g., which relations a sensor of a given class shall have), machine-checkable	the Brick community committee
instances	Brick graphs of concrete buildings (actual declarations of entities, relations, points)	deployment sites

Appendix

Table 36

Layer	RDF	OWL
syntax	✓triple syntax + URI	✓(inherited from RDF)
concepts	$\times$ (RDFS has only very weak class/property declarations)	✓TBox: class hierarchies and axioms
knowledge	$\times$	$\times$ the crucial gap: DL axioms are logical constraints on concepts, not promulgated norms of "how instances shall be and what deviation counts as"; there is no committee-promulgated industry operating procedure, and no institutionalized handling of violations
instances	✓triples	✓ABox

Appendix

Table 37

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Current large-language-model (LLM) physics benchmarks are usually scored by answer accuracy, which cannot distinguish genuine reasoning from recall of familiar problem patterns and reveals little about where a model's reasoning breaks down. We introduce an auditable four-stage diagnostic that evaluates whether an LLM can reason inside an unfamiliar physics framework through induction, formulation, prediction, and review. The diagnostic combines locked pre-registrations, fresh sessions between stages, dual-LLM judging, and a human-audit pathway, and we apply it to three parallel physics worlds: a single-equation counterfactual world (

F=mv

), a historical framework (Aristotelian mechanics), and a four-domain counterfactual world (Decay World). Across Claude Opus 4.7, GPT-5.5, and Gemini 3.1 Pro, the three worlds yield composite PASS rates are 6/15, 6/15, and 0/15 respectively (content

\land

structural for

F=mv

and Aristotelian, content axis only for Decay World where the structural axis is out of scope). The most pointed empirical pattern is a qualitative-versus-quantitative asymmetry: in Decay World, models almost never predict the wrong direction of change, but frequently compute the wrong ratio by slipping back to standard-physics relations. The protocol also surfaces two methodology findings: LLM-judge reliability does not transfer across frameworks, and Stage 4 self-review is weak in every framework, with the model's own review wrongly reporting no earlier error in at least two-thirds of the trials that actually contained one. We release the full prompts, responses, verdicts, and audit records.

Dong Zhang

LLM Evaluation Physical Reasoning Counterfactual Reasoning in Language Models Language Model Self-Assessment Counterfactual Reasoning

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