Pith Number

pith:YEDJXVTC

pith:2025:YEDJXVTC2IZJISRDUSFQZ7GLTT

not attested not anchored not stored refs pending

Refined thresholds for inconsistency: The effect of the graph associated with incomplete pairwise comparisons

Kolos Csaba \'Agoston, L\'aszl\'o Csat\'o

Inconsistency thresholds for incomplete pairwise comparisons depend on the graph of known comparisons.

arxiv:2510.27011 v4 · 2025-10-30 · stat.ME · math.OC

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\usepackage{pith}
\pithnumber{YEDJXVTC2IZJISRDUSFQZ7GLTT}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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 uncover that they depend not only on the size of the matrix and the number of missing entries, but also on the undirected graph whose edges represent the known pairwise comparisons.

C2weakest assumption

The inconsistency measure permits exact, graph-dependent thresholds that can be precomputed from the spectral radius without additional fitting or post-hoc adjustments for each matrix.

C3one line summary

Inconsistency thresholds for incomplete pairwise comparisons depend on the spectral radius of the graph formed by known entries, beyond matrix size and missing count.

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-25T02:02:09.858151Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c1069bd662d232944a23a48b0cfccb9cd27d7d3cbc81ea2dbe74ae98ea10a701

Aliases

arxiv: 2510.27011 · arxiv_version: 2510.27011v4 · doi: 10.48550/arxiv.2510.27011 · pith_short_12: YEDJXVTC2IZJ · pith_short_16: YEDJXVTC2IZJISRD · pith_short_8: YEDJXVTC

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/YEDJXVTC2IZJISRDUSFQZ7GLTT \
  | 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: c1069bd662d232944a23a48b0cfccb9cd27d7d3cbc81ea2dbe74ae98ea10a701

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1abffe6bf18426f61b1649cd97025ebfb99b0d9a6a420ef96ab0b2e1c7235b61",
    "cross_cats_sorted": [
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "stat.ME",
    "submitted_at": "2025-10-30T21:24:34Z",
    "title_canon_sha256": "1a1448776c6c4f1435603dbc513a85380dc3c574dc939546d91a88616c8dfc19"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2510.27011",
    "kind": "arxiv",
    "version": 4
  }
}