Pith Number

pith:PYVDSWJ6

pith:2025:PYVDSWJ6DXEGACWOPZZFXMP5T4

not attested not anchored not stored refs pending

The feasibility of multi-graph alignment: a Bayesian approach

Laurent Massouli\'e, Louis Vassaux

Above a critical threshold exact multi-graph alignment is achievable with high probability in the Gaussian model

arxiv:2502.17142 v4 · 2025-02-24 · math.ST · math.PR · stat.ML · stat.TH

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\usepackage{pith}
\pithnumber{PYVDSWJ6DXEGACWOPZZFXMP5T4}

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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

In the Gaussian model, above a critical threshold, exact alignment is achievable with high probability, while below it, even partial alignment is statistically impossible.

C2weakest assumption

The random multi-graph generative models (Gaussian weights and sparse Erdős-Rényi edges) correctly capture the statistical setting, and the newly developed Bayesian estimation framework over metric spaces yields the precise information-theoretic feasibility thresholds without hidden modeling assumptions.

C3one line summary

Establishes an all-or-nothing threshold for exact multi-graph alignment in the Gaussian model and a partial-alignment threshold in the sparse Erdős-Rényi model using a general Bayesian estimation framework over metric spaces.

Receipt and verification

First computed	2026-05-25T02:01:02.437895Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7e2a39593e1dc8600ace7e725bb1fd9f2363950bc12d4f76472d8a4980dff43a

Aliases

arxiv: 2502.17142 · arxiv_version: 2502.17142v4 · doi: 10.48550/arxiv.2502.17142 · pith_short_12: PYVDSWJ6DXEG · pith_short_16: PYVDSWJ6DXEGACWO · pith_short_8: PYVDSWJ6

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/PYVDSWJ6DXEGACWOPZZFXMP5T4 \
  | 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: 7e2a39593e1dc8600ace7e725bb1fd9f2363950bc12d4f76472d8a4980dff43a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "62bb47192f097c5cb5b69635b20c721967c72e9c6dc30936cd4f17c21c525acc",
    "cross_cats_sorted": [
      "math.PR",
      "stat.ML",
      "stat.TH"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2025-02-24T13:34:21Z",
    "title_canon_sha256": "b8916ac057f41d446b9f6158de9fee54cf4ecb00b802d8d9b265c3b0a7cea71d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2502.17142",
    "kind": "arxiv",
    "version": 4
  }
}