IndisputableMonolith.Gravity.Analysis.OrderSensitiveHistoryResponse4D
Finite 4D order-sensitive history response on the Freudenthal sixteen-site patch: antisymmetric seating, first-variation edge currents, and response differences that separate ordered Loom histories from classical metric strain. Gravity analysts cite it as the discrete gate before continuum residual promotion. The module defines fingerprints, seat generators, Dirac probes, and forward/reverse response lemmas used by the residual and audit layers.
claimOn the sixteen-site Freudenthal patch with Q3 seating (spatial axes in bits $0,1,2$, record-time in bit $3$), an antisymmetric edge generator induces a first-variation edge current (history response) for an ordered classical source pair. The forward-minus-reverse response difference is the finite order-sensitive residual, to be tested against linearized metric edge images $F$ arising as strain currents of $\mathrm{Mat}_4$ perturbations.
background
This module is the finite history-response layer of the Order-Sensitive Gravity proposition (frozen worlds G0/G1 and metric-null). Upstream, a classical source projection is a typed reading of a Loom Config allowed to stand in for the conventional-source half of the discovery discriminator, only when already proved equal on the gauge-separated quotient. Q3 patch seating packs Pattern-3 axes into bits 0,1,2 and record-time into bit 3 on the Fin-16 patch, without pulling the heavy gravity chain.
MetricEdgeImage F means $F$ is the strain current of some $\mathrm{Mat}_4$ perturbation on that patch; the strain formula and binary coordinates match the Freudenthal cover edge-current action. Loom separation supplies the kernel-checked witness that distinguishes legitimate one-way key/door structure from its security dual, used here to keep gauge-equivalent readings from contaminating the residual test.
Sibling objects include a polynomial fingerprint of natural-number lists, unit weights, Dirac probes on edges, seat generators, antisymmetric edge data, history response, response difference, and the first variation of the edge current.
proof idea
Definition-and-lemma module, not a single theorem. It introduces list fingerprints, antisymmetric edges, a distinguished seat generator, history response, response difference, edge-current first variation, Dirac probes, and unit weight. Short lemmas record that the seat generator is nontrivial, that antisymmetry flips under edge reversal, and that the forward history response is the corresponding first-variation evaluation. Downstream continuum and audit modules import this package as the finite gate; no continuum limit or trichotomy is proved here.
why it matters in Recognition Science
Parent consumers are the continuum order-sensitive residual (Campaign G4/G5) and the axiom audit for this module. The continuum layer replaces finite Boolean non-membership in MetricEdgeImage by a normalized-separation trichotomy under a shape-regular refinement family; it needs a clean finite residual built from ordered history response. The audit requires that the load-bearing finite gate report the base triple (or a subset) and reject silent sorryAx.
In the Recognition gravity stack this is the discrete witness that order of source seating is not absorbed by linearized metric strain on the eight-tick / D=3 Freudenthal patch. It sits between classical source projection, Q3 seating, and metric edge image on one side, and continuum residual promotion on the other, closing the finite half of the order-sensitive discriminator without yet claiming continuum separation.
scope and limits
- Does not prove continuum separation or the G4/G5 trichotomy.
- Does not construct or classify full MetricEdgeImage membership algorithms.
- Does not derive Einstein equations or fix G, c, or hbar.
- Does not claim the residual is nonzero for every source pair; only sets up the finite response.
- Does not import or discharge the heavy gravity analysis chain beyond seating and edge image.
used by (2)
depends on (4)
declarations in this module (25)
-
def
listFingerprint -
def
antisymEdge -
def
seatGen1 -
def
historyResponse -
def
responseDiff -
def
edgeCurrentFirstVariation -
def
diracProbe -
def
unitWeight -
theorem
seatGen1_ne -
theorem
antisymEdge_fwd -
theorem
antisymEdge_rev -
theorem
historyResponse_fwd -
theorem
historyResponse_rev -
theorem
fingerprint_separates_cfgAB -
theorem
historyResponse_separates_cfgAB -
theorem
finiteCertificate_cfgAB -
theorem
edgeCurrentFirstVariation_dirac -
theorem
edgeAction_separates_cfgAB -
theorem
responseDiff_fwd -
theorem
responseDiff_rev -
theorem
responseDiff_fwd_ne -
theorem
responseDiff_cfgAB_not_in_MetricEdgeImage -
theorem
decoy_depthOne_blind -
theorem
discovery_pair_is_certificate_cfgAB -
theorem
orderSensitive_finite_gate_cfgAB