Pith Number

pith:E5IJG7GY

pith:2026:E5IJG7GYVXJHMYG4NY3CDW4TOV

not attested not anchored not stored refs pending

Self-Attention as Transport: Limits of Symmetric Spectral Diagnostics

Diego Maniloff, Dominik Dahlem, Mac Misiura

Symmetric spectral diagnostics on attention operators cannot detect the direction of information flow.

arxiv:2605.04893 v2 · 2026-05-06 · cs.LG · cs.CL · stat.ML

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\pithnumber{E5IJG7GYVXJHMYG4NY3CDW4TOV}

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

we prove that every transpose-invariant spectral diagnostic of this operator is structurally orientation-blind (it cannot distinguish an operator from its transpose, and therefore cannot detect information-flow direction), with a quantitative converse establishing the asymmetry coefficient G as the unique control parameter for direction.

C2weakest assumption

That the dominant hallucination mechanisms in the tested benchmarks are fully captured by the transport capacity and directionality of the degree-normalized attention operator, without substantial confounding from other components such as feed-forward layers, layer norms, or output decoding.

C3one line summary

Symmetric spectral diagnostics on attention are structurally blind to flow direction, with asymmetry G as the sole control parameter, yielding a two-axis test that distinguishes bottleneck versus diffuse hallucination modes with opposite polarity.

Receipt and verification

First computed	2026-06-11T01:10:37.036050Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2750937cd8add27660dc6e3621db93755972ddd7418e16b4f168d52651881f7f

Aliases

arxiv: 2605.04893 · arxiv_version: 2605.04893v2 · doi: 10.48550/arxiv.2605.04893 · pith_short_12: E5IJG7GYVXJH · pith_short_16: E5IJG7GYVXJHMYG4 · pith_short_8: E5IJG7GY

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/E5IJG7GYVXJHMYG4NY3CDW4TOV \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 2750937cd8add27660dc6e3621db93755972ddd7418e16b4f168d52651881f7f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "64d62e44c9a479dbfba5e54ad412299368131d30c5975cd9de4c414c63e90a69",
    "cross_cats_sorted": [
      "cs.CL",
      "stat.ML"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-06T13:25:13Z",
    "title_canon_sha256": "ddfa9aca8572b4983032ef1141a1e649815c5b78164a84a850c110a01022939e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.04893",
    "kind": "arxiv",
    "version": 2
  }
}