{"paper":{"title":"The feasibility of multi-graph alignment: a Bayesian approach","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Above a critical threshold exact multi-graph alignment is achievable with high probability in the Gaussian model","cross_cats":["math.PR","stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Laurent Massouli\\'e, Louis Vassaux","submitted_at":"2025-02-24T13:34:21Z","abstract_excerpt":"We establish thresholds for the feasibility of random multi-graph alignment in two models. In the Gaussian model, we demonstrate an \"all-or-nothing\" phenomenon: above a critical threshold, exact alignment is achievable with high probability, while below it, even partial alignment is statistically impossible. In the sparse Erd\\H{o}s-R\\'enyi model, we rigorously identify a threshold below which no meaningful partial alignment is possible and conjecture that above this threshold, partial alignment can be achieved. To prove these results, we develop a general Bayesian estimation framework over met"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"In the Gaussian model, above a critical threshold, exact alignment is achievable with high probability, while below it, even partial alignment is statistically impossible.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"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.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"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.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Above a critical threshold exact multi-graph alignment is achievable with high probability in the Gaussian model","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"f897d2d319318f895a650808e71903da8d51be76c45735ccf2b8abf67a20c50f"},"source":{"id":"2502.17142","kind":"arxiv","version":4},"verdict":{"id":"8d07b913-4bf7-4f12-ae6a-ae2a2e82ef46","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-23T02:45:07.717673Z","strongest_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.","one_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.","pipeline_version":"pith-pipeline@v0.9.0","weakest_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.","pith_extraction_headline":"Above a critical threshold exact multi-graph alignment is achievable with high probability in the Gaussian model"},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.17142/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}