In plain words: four textbook dependence detectors โ Hoeffding's D, the ฯ* sign covariance, distance correlation, and the kernel test dHSIC โ were examined together, as the feed recommended. All four SEE the dependence between trading intensity and bar duration loud and clear (4 to 70 times their noise floors). And all four died the same death: the noise floor each one ships with assumes independent samples, and on market bars every one of them cries "signal!" on provably-null data far above its promised 5% โ Hoeffding's "exact" null the worst offender on record at 57%, and even distance correlation's block-shuffled null (the repair its own literature suggests) still fails at 24%, because short blocks can't fake long memory. The broken-certificate family the loop first spotted two kills ago now has six members โ law-grade. Two bonuses: the exam's own self-check caught a subtle bug in our ฯ* implementation (algebra says certain patterns score exactly zero; floating-point arithmetic said almost-zero, which the sign function turned into noise) โ caught, fixed, re-run, verdict unchanged; and the feed's prediction that these four cousins are interchangeable was refuted โ distance correlation turns out to be a genuinely different witness, which makes "distance correlation with the loop's own certified shift-based noise floor" the family's best re-proposal.
Preflight (A0): 2026-07-14 00:30 โ load1 4.34/32c ยท no heavy nasimubd jobs ยท 27 GiB avail, si/soโ0 ยท clickhouse active โ ALL PASS. Sync: main +11 โ 65-commit rebase conflicted; resolved per the generated-artifact rule as merge 18a0a3c2 (campaign folder OURS ยท other generated nav THEIRS ยท nav rebuilt). PR #599 OPEN. Three capped runs (2.37 + 0.36 + 0.60 min), readonly=2 loader, permutations/shifts/blocks of real values (03c). Operator directive 2026-07-14 recorded (row 112): finish evaluations โ handover (ADR live expiry + flowchart) โ PARK.
E2 โ own-null validity (THE KILL): pooled FA at nominal 5%, bar 10%
E3 reality (own shift null)
G0 echo
Verdict (row 113)
H-031 Hoeffding's D
56.6% โ the "exact distribution-free null" is exact only under iid; WORST certificate on record
44โ70ร
0.977 โ G0 DUPLICATE (doubly dead)
EXCLUDE ยท KILL #39
H-032 ฯ* (v2 corrected kernel)
11.1% โ the closest E2 call on record; the frozen rule fires
32โ36ร
0.916
EXCLUDE ยท KILL #40
H-033 distance correlation
24.2% โ with the feed-specified block(n1/3)-permutation null: block-length insufficiency โ short blocks can't reproduce long-range dependence
4.2โ4.8ร
0.59 โ the family's independent witness
EXCLUDE ยท KILL #41
H-034 dHSIC
39.1% โ permutation null
24โ30ร
0.83
EXCLUDE ยท KILL #42
Discoveries beyond the kills
#
Finding
1
ฮต-doctrine self-falsification #6 (caught by the HV gate, fixed in v2): 8 of 24 quadruple orderings of the ฯ* sign kernel are ALGEBRAICALLY zero but float to ยฑ1e-16 โ sign() emits ยฑ1 noise, inflating ฯ*(z,z) from the combinatorial 2/3 to 0.846. Tolerance-corrected kernel (|E| โค 1e-9 โ 0) restores the ceiling exactly. v1 ฯ* legs superseded append-only.
2
Ties discovery: 262/43/215 duplicate duration values per env โ the no-ties classical forms (D, ฯ*) are tie-sensitive; rank-invariance failures recorded as harness caveat, NOT candidate evidence (fed CRAN forms carry tie corrections).
3
The feed's mutual-echo prediction REFUTED: the cousins are NOT interchangeable (max sibling echo D~ฯ* 0.936; dcor 0.50โ0.70 vs all) โ four different witnesses, one broken certificate class.
4
RE-PROPOSAL filed (constructive residue): dcor (and ฯ*) + the campaign's one CERTIFIED null machinery โ the circular-shift null (row 100, FWER 0/49). Real reading, independent witness, valid floor. Queued for the operator, not self-admitted.
The IID-certificate class โ six members, LAW-GRADE
#
Certificate
Promised ฮฑ
Actual FA
Row
1
HAC-t p-values
5%
43.4%
99
2
ฯยฒ(12) closed-form TE null
5%
16.2%
111
3
Hoeffding's D "exact" null
5%
56.6%
113
4
ฯ* iid null
5%
11.1%
113
5
dcor block(n1/3)-perm null
5%
24.2%
113
6
dHSIC perm null
5%
39.1%
113
Proposed standing law (operator ratification pending): independence-assuming nulls โ closed-form, permutation, or short-block โ are inadmissible p-sources on this substrate. The certified counter-example remains the de-aligned circular-shift null (row 100).
โถ Next iteration
Next firing: B-02 advances to H-055 SKIT (sequential kernelized independence, anytime-valid e-process) โ the certificate attack travels to its optional-continuation guarantee: is the e-process actually safe on autocorrelated bars? Then H-050 Effective TE + H-035 copula entropy (grouped: information-magnitude, shuffle-null class), then H-041 BROJA-2PID + H-042 O-information (grouped, constructed-anchor, last) โ B-02 then CLOSES and the operator's 2026-07-14 handover directive executes: full metrics inventory + ADR-LIVE-EXPIRY + implementation flowchart, then the loop PARKS.Standing for the operator: tri-tier ratification (row 105) ยท 5-sighting tail-invariance (rows 104โ109) ยท IID-CERTIFICATE LAW โ 6 members (rows 99/111/113) ยท dcor/ฯ*-with-shift-null re-proposal (row 113) ยท RW+MCS pipeline ยท H-005 full-window re-proposal ยท 03c wild gray zone ยท M4-bar question ยท H-062 ยท inverted-mechanism ยท 73 cycle-1 drafts ยท Frontier #4 (gates B-05, 11 items) ยท STABLE-declaration ยท boneyard counter ยท PR #599 โ B-02 now 0 admits ยท 5 kills ยท 5 queued.