{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:JK7WNMMZ6ZLN3AGDVFKVWGZFTK","short_pith_number":"pith:JK7WNMMZ","canonical_record":{"source":{"id":"2505.20954","kind":"arxiv","version":5},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2025-05-27T09:50:00Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"23daad944e2c0abda28397542a76a225eb81716e3805e7977d970105401d50e4","abstract_canon_sha256":"6919c771b88ecd6a0c5cfe21a87110f08c527198227e2f76c956767267431176"},"schema_version":"1.0"},"canonical_sha256":"4abf66b199f656dd80c3a9555b1b259abc33bd941ffc7288446102f60416f170","source":{"kind":"arxiv","id":"2505.20954","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.20954","created_at":"2026-06-30T01:16:23Z"},{"alias_kind":"arxiv_version","alias_value":"2505.20954v5","created_at":"2026-06-30T01:16:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.20954","created_at":"2026-06-30T01:16:23Z"},{"alias_kind":"pith_short_12","alias_value":"JK7WNMMZ6ZLN","created_at":"2026-06-30T01:16:23Z"},{"alias_kind":"pith_short_16","alias_value":"JK7WNMMZ6ZLN3AGD","created_at":"2026-06-30T01:16:23Z"},{"alias_kind":"pith_short_8","alias_value":"JK7WNMMZ","created_at":"2026-06-30T01:16:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:JK7WNMMZ6ZLN3AGDVFKVWGZFTK","target":"record","payload":{"canonical_record":{"source":{"id":"2505.20954","kind":"arxiv","version":5},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2025-05-27T09:50:00Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"23daad944e2c0abda28397542a76a225eb81716e3805e7977d970105401d50e4","abstract_canon_sha256":"6919c771b88ecd6a0c5cfe21a87110f08c527198227e2f76c956767267431176"},"schema_version":"1.0"},"canonical_sha256":"4abf66b199f656dd80c3a9555b1b259abc33bd941ffc7288446102f60416f170","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-30T01:16:23.500589Z","signature_b64":"4NCYQM9kBb14yAlv474dQCYucDvaY9NjCN0pampSiMMn5EG6op4xr9YQdY4IoRKfKH0pAvoIQ8v/Dasw6jz7AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4abf66b199f656dd80c3a9555b1b259abc33bd941ffc7288446102f60416f170","last_reissued_at":"2026-06-30T01:16:23.499742Z","signature_status":"signed_v1","first_computed_at":"2026-06-30T01:16:23.499742Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.20954","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-30T01:16:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QvKGg1zRvsU0NzNJ++tfi1d8usq0GMitFoumPVsnXPI64vQcZUbt6zmJO2EKBNzd3nhCh7jBG/VDOMDPpwetDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T05:48:29.652609Z"},"content_sha256":"00dc0686b136dd0a1c2cf27605b8e9566c0d82b71972a28f3a1add0712c7643f","schema_version":"1.0","event_id":"sha256:00dc0686b136dd0a1c2cf27605b8e9566c0d82b71972a28f3a1add0712c7643f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:JK7WNMMZ6ZLN3AGDVFKVWGZFTK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Finding the right path: statistical mechanics of connected solutions in constraint satisfaction problems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A new statistical mechanics ensemble reveals a stable cluster of connected solutions in the symmetric binary perceptron that persists up to a critical threshold.","cross_cats":["cond-mat.stat-mech"],"primary_cat":"cond-mat.dis-nn","authors_text":"Damien Barbier","submitted_at":"2025-05-27T09:50:00Z","abstract_excerpt":"We define and study a statistical mechanics ensemble that characterizes connected solutions in constraint satisfaction problems (CSPs). Built around a well-known local entropy bias, it allows us to better identify hardness transitions in problems where the energy landscape is dominated by isolated solutions. We apply this new device to the symmetric binary perceptron model (SBP), and study how its manifold of connected solutions behaves. We choose this particular problem because, while its typical solutions are isolated, it can be solved using local algorithms for a certain range of constraint"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We unveil the presence of a cluster composed of delocalized connected solutions. In particular, we demonstrate its stability until a critical threshold κ^{no-mem}_{loc. stab.} (dependent on α).","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The local entropy bias is assumed to correctly identify the manifold of connected solutions whose stability governs algorithmic success in the symmetric binary perceptron.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A new ensemble for connected solutions in CSPs reveals a stable cluster of delocalized solutions in the symmetric binary perceptron up to a critical threshold κ_no-mem_loc.stab. that conventional approaches miss.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A new statistical mechanics ensemble reveals a stable cluster of connected solutions in the symmetric binary perceptron that persists up to a critical threshold.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"caef09cc65fcf9db773440371e1ccfeb02d296f4e193d97e738c985276f9cb45"},"source":{"id":"2505.20954","kind":"arxiv","version":5},"verdict":{"id":"a258c5d6-2836-451b-8f87-a201c9d81492","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T13:35:17.335214Z","strongest_claim":"We unveil the presence of a cluster composed of delocalized connected solutions. In particular, we demonstrate its stability until a critical threshold κ^{no-mem}_{loc. stab.} (dependent on α).","one_line_summary":"A new ensemble for connected solutions in CSPs reveals a stable cluster of delocalized solutions in the symmetric binary perceptron up to a critical threshold κ_no-mem_loc.stab. that conventional approaches miss.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The local entropy bias is assumed to correctly identify the manifold of connected solutions whose stability governs algorithmic success in the symmetric binary perceptron.","pith_extraction_headline":"A new statistical mechanics ensemble reveals a stable cluster of connected solutions in the symmetric binary perceptron that persists up to a critical threshold."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.20954/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"},"verdict_id":"a258c5d6-2836-451b-8f87-a201c9d81492"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-30T01:16:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uaW8fAivjE7rAOd9OaCkReRTF901uzb+ZeEUWDxEMyTQxmGXogYTK7N6nx6wrq6vVky35OVpsIIIgPzBJqoMDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T05:48:29.653375Z"},"content_sha256":"b26119e410d7467b5deb156cd999d401d7722ede2d678cdb109eb36691d265b2","schema_version":"1.0","event_id":"sha256:b26119e410d7467b5deb156cd999d401d7722ede2d678cdb109eb36691d265b2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JK7WNMMZ6ZLN3AGDVFKVWGZFTK/bundle.json","state_url":"https://pith.science/pith/JK7WNMMZ6ZLN3AGDVFKVWGZFTK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JK7WNMMZ6ZLN3AGDVFKVWGZFTK/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-06T05:48:29Z","links":{"resolver":"https://pith.science/pith/JK7WNMMZ6ZLN3AGDVFKVWGZFTK","bundle":"https://pith.science/pith/JK7WNMMZ6ZLN3AGDVFKVWGZFTK/bundle.json","state":"https://pith.science/pith/JK7WNMMZ6ZLN3AGDVFKVWGZFTK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JK7WNMMZ6ZLN3AGDVFKVWGZFTK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:JK7WNMMZ6ZLN3AGDVFKVWGZFTK","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"6919c771b88ecd6a0c5cfe21a87110f08c527198227e2f76c956767267431176","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2025-05-27T09:50:00Z","title_canon_sha256":"23daad944e2c0abda28397542a76a225eb81716e3805e7977d970105401d50e4"},"schema_version":"1.0","source":{"id":"2505.20954","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.20954","created_at":"2026-06-30T01:16:23Z"},{"alias_kind":"arxiv_version","alias_value":"2505.20954v5","created_at":"2026-06-30T01:16:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.20954","created_at":"2026-06-30T01:16:23Z"},{"alias_kind":"pith_short_12","alias_value":"JK7WNMMZ6ZLN","created_at":"2026-06-30T01:16:23Z"},{"alias_kind":"pith_short_16","alias_value":"JK7WNMMZ6ZLN3AGD","created_at":"2026-06-30T01:16:23Z"},{"alias_kind":"pith_short_8","alias_value":"JK7WNMMZ","created_at":"2026-06-30T01:16:23Z"}],"graph_snapshots":[{"event_id":"sha256:b26119e410d7467b5deb156cd999d401d7722ede2d678cdb109eb36691d265b2","target":"graph","created_at":"2026-06-30T01:16:23Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"We unveil the presence of a cluster composed of delocalized connected solutions. In particular, we demonstrate its stability until a critical threshold κ^{no-mem}_{loc. stab.} (dependent on α)."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The local entropy bias is assumed to correctly identify the manifold of connected solutions whose stability governs algorithmic success in the symmetric binary perceptron."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"A new ensemble for connected solutions in CSPs reveals a stable cluster of delocalized solutions in the symmetric binary perceptron up to a critical threshold κ_no-mem_loc.stab. that conventional approaches miss."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"A new statistical mechanics ensemble reveals a stable cluster of connected solutions in the symmetric binary perceptron that persists up to a critical threshold."}],"snapshot_sha256":"caef09cc65fcf9db773440371e1ccfeb02d296f4e193d97e738c985276f9cb45"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2505.20954/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We define and study a statistical mechanics ensemble that characterizes connected solutions in constraint satisfaction problems (CSPs). Built around a well-known local entropy bias, it allows us to better identify hardness transitions in problems where the energy landscape is dominated by isolated solutions. We apply this new device to the symmetric binary perceptron model (SBP), and study how its manifold of connected solutions behaves. We choose this particular problem because, while its typical solutions are isolated, it can be solved using local algorithms for a certain range of constraint","authors_text":"Damien Barbier","cross_cats":["cond-mat.stat-mech"],"headline":"A new statistical mechanics ensemble reveals a stable cluster of connected solutions in the symmetric binary perceptron that persists up to a critical threshold.","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2025-05-27T09:50:00Z","title":"Finding the right path: statistical mechanics of connected solutions in constraint satisfaction problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.20954","kind":"arxiv","version":5},"verdict":{"created_at":"2026-05-19T13:35:17.335214Z","id":"a258c5d6-2836-451b-8f87-a201c9d81492","model_set":{"reader":"grok-4.3"},"one_line_summary":"A new ensemble for connected solutions in CSPs reveals a stable cluster of delocalized solutions in the symmetric binary perceptron up to a critical threshold κ_no-mem_loc.stab. that conventional approaches miss.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"A new statistical mechanics ensemble reveals a stable cluster of connected solutions in the symmetric binary perceptron that persists up to a critical threshold.","strongest_claim":"We unveil the presence of a cluster composed of delocalized connected solutions. In particular, we demonstrate its stability until a critical threshold κ^{no-mem}_{loc. stab.} (dependent on α).","weakest_assumption":"The local entropy bias is assumed to correctly identify the manifold of connected solutions whose stability governs algorithmic success in the symmetric binary perceptron."}},"verdict_id":"a258c5d6-2836-451b-8f87-a201c9d81492"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:00dc0686b136dd0a1c2cf27605b8e9566c0d82b71972a28f3a1add0712c7643f","target":"record","created_at":"2026-06-30T01:16:23Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"6919c771b88ecd6a0c5cfe21a87110f08c527198227e2f76c956767267431176","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2025-05-27T09:50:00Z","title_canon_sha256":"23daad944e2c0abda28397542a76a225eb81716e3805e7977d970105401d50e4"},"schema_version":"1.0","source":{"id":"2505.20954","kind":"arxiv","version":5}},"canonical_sha256":"4abf66b199f656dd80c3a9555b1b259abc33bd941ffc7288446102f60416f170","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4abf66b199f656dd80c3a9555b1b259abc33bd941ffc7288446102f60416f170","first_computed_at":"2026-06-30T01:16:23.499742Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-30T01:16:23.499742Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4NCYQM9kBb14yAlv474dQCYucDvaY9NjCN0pampSiMMn5EG6op4xr9YQdY4IoRKfKH0pAvoIQ8v/Dasw6jz7AQ==","signature_status":"signed_v1","signed_at":"2026-06-30T01:16:23.500589Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.20954","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:00dc0686b136dd0a1c2cf27605b8e9566c0d82b71972a28f3a1add0712c7643f","sha256:b26119e410d7467b5deb156cd999d401d7722ede2d678cdb109eb36691d265b2"],"state_sha256":"75daa7105d751df6bddf13f8f71f533e74b6500693afff36a5beb359b999423d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L3zVVdTH/8KXsWGrXqxIipvWpBNZ/R33uKXg9JuL/4rrCP5Q2ws6/tlbrClBj+4kC9j2wSoSjlWhKAmIsj/5AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T05:48:29.659408Z","bundle_sha256":"e5bbc48bf07ed948474afa826b4b1328a348d616f7f410d54bbaf9d161154182"}}