PURIQ /formulas — 23 FormulaAgents

Experimental kernel-verified waves (NOT in the locked count of 8; honest maturity labels):
• wave5 (+11 thm, PR#186) [proven sorry-free (experimental)]: Tsirelson/CHSH governance ceiling, AM-GM no-inflation, Cauchy-Schwarz similarity, conformal count law, collision pigeonhole, optional-stopping audit core. 6 Mathlib-dep CI-green + 5 bare-lean.
• wave6 (+11 thm, PR#189) [proven sorry-free (experimental)]: Graph substrate: F-G4 Lambda-graph isomorphism invariance (CI-green), F-G1 Kuratowski embedding, F-G3 geometric contraction, F-G2 GNN<=1-WL ceiling, F-G5 bounded-frontier DAG termination, F-G6 relabel-invariant functionals.
• wave7 (+10 thm, PR#190) [proven sorry-free (experimental)]: Conformal rank-count p-value (distribution-free Trust Score interval, anti-overconfidence floor), two-sided Doob audit envelope, degree-sum iso-invariance, PAC-Bayes/router envelope (min<=avg<=max).
• agentic_loop (+28 thm, PR#188) [proven sorry-free (experimental); P5 axiom-gated (declared)]: End-to-end governed-run system proofs P1-P6: receipt completeness, gate-soundness, non-interference (injection-resistant), replay determinism, tamper-evidence (axiom-gated on hash collision-resistance), monotone auditability. 1 declared hash axiom (P5).
Trust Score interval: sourced from CONFORMAL (W5-3 + W7-4) — distribution-free, with an anti-overconfidence floor (we never report 100%). NOT Hoeffding/PAC-Bayes (those are NOT proven at the pinned Mathlib v4.13.0).
Deferred (not proven at pin): C3 Hoeffding, C4 Azuma, C5 KL≥0, C15, C16, C18, C19.

ID	Formula	Organ	Live value	Identity	Lean class	Proof status	Harness	Chain	Invoked by
F1 ¶	Euler-Khipu DAG Identity	Khipu	`-1`	OK	PROVED	PROVED [lean: rfl]	100/100	yes	Khipu
click loads the LIVE per-formula endpoint — raw output, fetched fresh on every open
F2 ¶	Egyptian-Kallpa Allocation	Kallpa	`2`	OK	SKELETON	UNATTEMPTED	100/100	yes	Kallpa
click loads the LIVE per-formula endpoint — raw output, fetched fresh on every open
F3 ¶	Noether-Khipu Conservation	Khipu	`6.1836`	OK	SORRY	UNATTEMPTED	100/100	yes	Khipu
click loads the LIVE per-formula endpoint — raw output, fetched fresh on every open
F4 ¶	Gauss-Yuyay Aggregation	Yuyay	`0.786113`	OK	PROVED	PROVED [lean: induction]	100/100	yes	Yuyay
click loads the LIVE per-formula endpoint — raw output, fetched fresh on every open
F5 ¶	Euler-Lagrange Agency	A/agency	`-0.0`	OK	SKELETON	UNATTEMPTED	100/100	yes	A/agency
click loads the LIVE per-formula endpoint — raw output, fetched fresh on every open
F6 ¶	Newton Risk-Velocity Tripwire	HUKLLA	`1.1767`	OK	SKELETON	UNATTEMPTED	100/100	yes	HUKLLA
click loads the LIVE per-formula endpoint — raw output, fetched fresh on every open
F7 ¶	Inverse-Square/Zeta Provenance	Khipu/Kallpa	`1.3415`	OK	PROVED	PROVED [lean: rw]	100/100	yes	Khipu, Kallpa
click loads the LIVE per-formula endpoint — raw output, fetched fresh on every open
F8 ¶	Newton-Parsimony Pick	HUKLLA	`d`	OK	SKELETON	UNATTEMPTED	100/100	yes	HUKLLA
click loads the LIVE per-formula endpoint — raw output, fetched fresh on every open
F9 ¶	Sulba Yuyay Mass-Conservation	Yuyay	`-1.3429`	OK	SORRY	UNATTEMPTED	100/100	yes	Yuyay
click loads the LIVE per-formula endpoint — raw output, fetched fresh on every open
F10 ¶	Baudhayana Orthogonality Bound	Lambda-spine	`1.414215686`	OK	SORRY	UNATTEMPTED	100/100	yes	Lambda-spine
click loads the LIVE per-formula endpoint — raw output, fetched fresh on every open
F11 ¶	Frustum A-Shrink Law	A	`12.3429`	OK	PROVED	PROVED [lean: simp]	100/100	yes	A/agency
click loads the LIVE per-formula endpoint — raw output, fetched fresh on every open
F12 ¶	CRT-Hukulla Schedule	HUKLLA	`28`	OK	PROVED	PROVED [lean: rfl]	100/100	yes	HUKLLA
click loads the LIVE per-formula endpoint — raw output, fetched fresh on every open
F13 ¶	Gauss-Bonnet Spine Curvature	Lambda-spine	`12.566371`	OK	CONJ	UNATTEMPTED	100/100	yes	Lambda-spine
click loads the LIVE per-formula endpoint — raw output, fetched fresh on every open
F14 ¶	Ramanujan A-Partition Bound	A	`3010`	OK	CONJ	UNATTEMPTED	100/100	yes	A/agency
click loads the LIVE per-formula endpoint — raw output, fetched fresh on every open
F15 ¶	Grothendieck Organ Functor	compose	`-36.9881`	OK	SKELETON	UNATTEMPTED	100/100	yes	compose
click loads the LIVE per-formula endpoint — raw output, fetched fresh on every open
F16 ¶	von-Neumann-Hukulla Minimax	HUKLLA	`-2.6794`	OK	SKELETON	UNATTEMPTED	100/100	yes	HUKLLA
click loads the LIVE per-formula endpoint — raw output, fetched fresh on every open
F17 ¶	Shannon-Kallpa Capacity	Kallpa	`2.3754`	OK	SKELETON	UNATTEMPTED	100/100	yes	Kallpa
click loads the LIVE per-formula endpoint — raw output, fetched fresh on every open
F18 ¶	Kolmogorov A-Description Cap	A	`1`	OK	PROVED	PROVED [lean: rfl]	100/100	yes	A/agency
click loads the LIVE per-formula endpoint — raw output, fetched fresh on every open
F19 ¶	Turing-Fuel Halting Safety	core	`37`	OK	PROVED	PROVED [lean: rfl]	100/100	yes	PURIQ-core
click loads the LIVE per-formula endpoint — raw output, fetched fresh on every open
F20 ¶	Schrodinger Action Superposition	A	`1.0`	OK	SORRY	UNATTEMPTED	100/100	yes	A/agency
click loads the LIVE per-formula endpoint — raw output, fetched fresh on every open
F21 ¶	Dirac-Commit Projection	Khipu	`1.0`	OK	SORRY	UNATTEMPTED	100/100	yes	Khipu
click loads the LIVE per-formula endpoint — raw output, fetched fresh on every open
F22 ¶	Feynman-Puriq Path Integral	A	`2.74`	OK	PROVED	PROVED [lean: induction]	100/100	yes	A/agency
click loads the LIVE per-formula endpoint — raw output, fetched fresh on every open
F23 ¶	Bekenstein A-Cap	A	`1.2702`	OK	CONJ	CONJECTURE_1	100/100	yes	A/agency
click loads the LIVE per-formula endpoint — raw output, fetched fresh on every open

Formula

Organ

Live value

Identity

Lean class

Proof status

Harness

Chain

Invoked by

F1 ¶

Euler-Khipu DAG Identity

Khipu

-1

PROVED

PROVED [lean: rfl]

100/100

yes

Khipu

click loads the LIVE per-formula endpoint — raw output, fetched fresh on every open

F2 ¶

Egyptian-Kallpa Allocation

Kallpa

2

SKELETON

UNATTEMPTED

100/100

yes

Kallpa

click loads the LIVE per-formula endpoint — raw output, fetched fresh on every open

F3 ¶

Noether-Khipu Conservation

Khipu

6.1836

SORRY

UNATTEMPTED

100/100

yes

Khipu

click loads the LIVE per-formula endpoint — raw output, fetched fresh on every open

F4 ¶

Gauss-Yuyay Aggregation

Yuyay

0.786113

PROVED

PROVED [lean: induction]

100/100

yes

Yuyay

click loads the LIVE per-formula endpoint — raw output, fetched fresh on every open

F5 ¶

Euler-Lagrange Agency

A/agency

-0.0

SKELETON

UNATTEMPTED

100/100

yes

A/agency

click loads the LIVE per-formula endpoint — raw output, fetched fresh on every open

F6 ¶

Newton Risk-Velocity Tripwire

HUKLLA

1.1767

SKELETON

UNATTEMPTED

100/100

yes

HUKLLA

click loads the LIVE per-formula endpoint — raw output, fetched fresh on every open

F7 ¶

Inverse-Square/Zeta Provenance

Khipu/Kallpa

1.3415

PROVED

PROVED [lean: rw]

100/100

yes

Khipu, Kallpa

click loads the LIVE per-formula endpoint — raw output, fetched fresh on every open

F8 ¶

Newton-Parsimony Pick

HUKLLA

d

SKELETON

UNATTEMPTED

100/100

yes

HUKLLA

click loads the LIVE per-formula endpoint — raw output, fetched fresh on every open

F9 ¶

Sulba Yuyay Mass-Conservation

Yuyay

-1.3429

SORRY

UNATTEMPTED

100/100

yes

Yuyay

click loads the LIVE per-formula endpoint — raw output, fetched fresh on every open

F10 ¶

Baudhayana Orthogonality Bound

Lambda-spine

1.414215686

SORRY

UNATTEMPTED

100/100

yes

Lambda-spine

click loads the LIVE per-formula endpoint — raw output, fetched fresh on every open

F11 ¶

Frustum A-Shrink Law

12.3429

PROVED

PROVED [lean: simp]

100/100

yes

A/agency

click loads the LIVE per-formula endpoint — raw output, fetched fresh on every open

F12 ¶

CRT-Hukulla Schedule

HUKLLA

28

PROVED

PROVED [lean: rfl]

100/100

yes

HUKLLA

click loads the LIVE per-formula endpoint — raw output, fetched fresh on every open

F13 ¶

Gauss-Bonnet Spine Curvature

Lambda-spine

12.566371

CONJ

UNATTEMPTED

100/100

yes

Lambda-spine

click loads the LIVE per-formula endpoint — raw output, fetched fresh on every open

F14 ¶

Ramanujan A-Partition Bound

3010

CONJ

UNATTEMPTED

100/100

yes

A/agency

click loads the LIVE per-formula endpoint — raw output, fetched fresh on every open

F15 ¶

Grothendieck Organ Functor

compose

-36.9881

SKELETON

UNATTEMPTED

100/100

yes

compose

click loads the LIVE per-formula endpoint — raw output, fetched fresh on every open

F16 ¶

von-Neumann-Hukulla Minimax

HUKLLA

-2.6794

SKELETON

UNATTEMPTED

100/100

yes

HUKLLA

click loads the LIVE per-formula endpoint — raw output, fetched fresh on every open

F17 ¶

Shannon-Kallpa Capacity

Kallpa

2.3754

SKELETON

UNATTEMPTED

100/100

yes

Kallpa

click loads the LIVE per-formula endpoint — raw output, fetched fresh on every open

F18 ¶

Kolmogorov A-Description Cap

1

PROVED

PROVED [lean: rfl]

100/100

yes

A/agency

click loads the LIVE per-formula endpoint — raw output, fetched fresh on every open

F19 ¶

Turing-Fuel Halting Safety

core

37

PROVED

PROVED [lean: rfl]

100/100

yes

PURIQ-core

click loads the LIVE per-formula endpoint — raw output, fetched fresh on every open

F20 ¶

Schrodinger Action Superposition

1.0

SORRY

UNATTEMPTED

100/100

yes

A/agency

click loads the LIVE per-formula endpoint — raw output, fetched fresh on every open

F21 ¶

Dirac-Commit Projection

Khipu

1.0

SORRY

UNATTEMPTED

100/100

yes

Khipu

click loads the LIVE per-formula endpoint — raw output, fetched fresh on every open

F22 ¶

Feynman-Puriq Path Integral

2.74

PROVED

PROVED [lean: induction]

100/100

yes

A/agency

click loads the LIVE per-formula endpoint — raw output, fetched fresh on every open

F23 ¶

Bekenstein A-Cap

1.2702

CONJ

CONJECTURE_1

100/100

yes

A/agency

click loads the LIVE per-formula endpoint — raw output, fetched fresh on every open

Locked-proven (F1, F4, F7, F11, F12, F18, F19, F22): F1/F11/F12/F18/F19 proved in the local self-prove sprint (real local Lean v4.13.0, Mathlib-free); F4/F7/F22 locked kernel theorems (lutar-lean #219 / platform #321). Axioms: F11/F12 use propext (Lean core); F1/F18/F19 use none. No sorryAx. Lambda-uniqueness is Conjecture 1, NOT a theorem. Values recompute live per request. ADDITIVE only; IP-HOLD a11oy#57 untouched.