{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:YLFKVKANL7WS6NDOLUMDRF6ZF2","short_pith_number":"pith:YLFKVKAN","canonical_record":{"source":{"id":"2506.02652","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2025-06-03T09:04:04Z","cross_cats_sorted":[],"title_canon_sha256":"f7505de83070cb2927591dc0d7d17d6682e318e5c0c75610b35025bc75b2a847","abstract_canon_sha256":"dd801764b43fbfa8c426968a9127cd950943698d038d0b5d8b3d481cb750d182"},"schema_version":"1.0"},"canonical_sha256":"c2caaaa80d5fed2f346e5d183897d92e9b9ade9ad377f35a179e16ecb3d7da88","source":{"kind":"arxiv","id":"2506.02652","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.02652","created_at":"2026-07-05T11:15:05Z"},{"alias_kind":"arxiv_version","alias_value":"2506.02652v1","created_at":"2026-07-05T11:15:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.02652","created_at":"2026-07-05T11:15:05Z"},{"alias_kind":"pith_short_12","alias_value":"YLFKVKANL7WS","created_at":"2026-07-05T11:15:05Z"},{"alias_kind":"pith_short_16","alias_value":"YLFKVKANL7WS6NDO","created_at":"2026-07-05T11:15:05Z"},{"alias_kind":"pith_short_8","alias_value":"YLFKVKAN","created_at":"2026-07-05T11:15:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:YLFKVKANL7WS6NDOLUMDRF6ZF2","target":"record","payload":{"canonical_record":{"source":{"id":"2506.02652","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2025-06-03T09:04:04Z","cross_cats_sorted":[],"title_canon_sha256":"f7505de83070cb2927591dc0d7d17d6682e318e5c0c75610b35025bc75b2a847","abstract_canon_sha256":"dd801764b43fbfa8c426968a9127cd950943698d038d0b5d8b3d481cb750d182"},"schema_version":"1.0"},"canonical_sha256":"c2caaaa80d5fed2f346e5d183897d92e9b9ade9ad377f35a179e16ecb3d7da88","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:15:05.959379Z","signature_b64":"8dSNq3SiJb7HoWokfg0HEhAiwwTUASRhBI3nkbDTdGGOstpstF3lfjZNwZId2UIdGsHn+hjd/wuXN3q9PjdZBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c2caaaa80d5fed2f346e5d183897d92e9b9ade9ad377f35a179e16ecb3d7da88","last_reissued_at":"2026-07-05T11:15:05.958862Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:15:05.958862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.02652","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:15:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q8fkDQMHCuhAKMtE6Y9W9cGXXJAazUIifCRw9NoShBKPnLQqrJ09EjQRKcM9nYAQZEebqobtHVk2LQD0xY3zCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T08:04:12.633665Z"},"content_sha256":"16ae8776fa5f21f40c425f137c6cf498bd6294ce8d0cfe747552c81cd4021379","schema_version":"1.0","event_id":"sha256:16ae8776fa5f21f40c425f137c6cf498bd6294ce8d0cfe747552c81cd4021379"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:YLFKVKANL7WS6NDOLUMDRF6ZF2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Not every graph can be reconstructed from its boundary distance matrix","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ignacio M. Pelayo, Jos\\'e C\\'aceres","submitted_at":"2025-06-03T09:04:04Z","abstract_excerpt":"A vertex $v$ of a connected graph $G$ is said to be a boundary vertex of $G$ if for some other vertex $u$ of $G$, no neighbor of $v$ is further away from $u$ than $v$. The boundary $\\partial(G)$ of $G$ is the set of all of its boundary vertices.\n  The boundary distance matrix $\\hat{D}_G$ of a graph $G=([n],E)$ is the square matrix of order $\\kappa$, being $\\kappa$ the order of $\\partial(G)$, such that for every $i,j\\in \\partial(G)$, $[\\hat{D}_G]_{ij}=d_G(i,j)$.\n  In a recent paper [doi.org/10.7151/dmgt.2567], it was shown that if a graph $G$ is either a block graph or a unicyclic graph, then $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.02652","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.02652/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":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:15:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8Aopwye/WahNI+qId6MPepGVijBX4uVx+z0OzKl1Rwi993/hJoWRjFppUaqi1+821R2hls9B1IsjnVxXo7EbAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T08:04:12.634183Z"},"content_sha256":"e7086341512ccdf439343f531a388039596d567435309b971501b695e24ca614","schema_version":"1.0","event_id":"sha256:e7086341512ccdf439343f531a388039596d567435309b971501b695e24ca614"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YLFKVKANL7WS6NDOLUMDRF6ZF2/bundle.json","state_url":"https://pith.science/pith/YLFKVKANL7WS6NDOLUMDRF6ZF2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YLFKVKANL7WS6NDOLUMDRF6ZF2/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":"2026-08-06T08:04:12Z","links":{"resolver":"https://pith.science/pith/YLFKVKANL7WS6NDOLUMDRF6ZF2","bundle":"https://pith.science/pith/YLFKVKANL7WS6NDOLUMDRF6ZF2/bundle.json","state":"https://pith.science/pith/YLFKVKANL7WS6NDOLUMDRF6ZF2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YLFKVKANL7WS6NDOLUMDRF6ZF2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:YLFKVKANL7WS6NDOLUMDRF6ZF2","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":"dd801764b43fbfa8c426968a9127cd950943698d038d0b5d8b3d481cb750d182","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2025-06-03T09:04:04Z","title_canon_sha256":"f7505de83070cb2927591dc0d7d17d6682e318e5c0c75610b35025bc75b2a847"},"schema_version":"1.0","source":{"id":"2506.02652","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.02652","created_at":"2026-07-05T11:15:05Z"},{"alias_kind":"arxiv_version","alias_value":"2506.02652v1","created_at":"2026-07-05T11:15:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.02652","created_at":"2026-07-05T11:15:05Z"},{"alias_kind":"pith_short_12","alias_value":"YLFKVKANL7WS","created_at":"2026-07-05T11:15:05Z"},{"alias_kind":"pith_short_16","alias_value":"YLFKVKANL7WS6NDO","created_at":"2026-07-05T11:15:05Z"},{"alias_kind":"pith_short_8","alias_value":"YLFKVKAN","created_at":"2026-07-05T11:15:05Z"}],"graph_snapshots":[{"event_id":"sha256:e7086341512ccdf439343f531a388039596d567435309b971501b695e24ca614","target":"graph","created_at":"2026-07-05T11:15:05Z","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":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2506.02652/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A vertex $v$ of a connected graph $G$ is said to be a boundary vertex of $G$ if for some other vertex $u$ of $G$, no neighbor of $v$ is further away from $u$ than $v$. The boundary $\\partial(G)$ of $G$ is the set of all of its boundary vertices.\n  The boundary distance matrix $\\hat{D}_G$ of a graph $G=([n],E)$ is the square matrix of order $\\kappa$, being $\\kappa$ the order of $\\partial(G)$, such that for every $i,j\\in \\partial(G)$, $[\\hat{D}_G]_{ij}=d_G(i,j)$.\n  In a recent paper [doi.org/10.7151/dmgt.2567], it was shown that if a graph $G$ is either a block graph or a unicyclic graph, then $","authors_text":"Ignacio M. Pelayo, Jos\\'e C\\'aceres","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2025-06-03T09:04:04Z","title":"Not every graph can be reconstructed from its boundary distance matrix"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.02652","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:16ae8776fa5f21f40c425f137c6cf498bd6294ce8d0cfe747552c81cd4021379","target":"record","created_at":"2026-07-05T11:15:05Z","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":"dd801764b43fbfa8c426968a9127cd950943698d038d0b5d8b3d481cb750d182","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2025-06-03T09:04:04Z","title_canon_sha256":"f7505de83070cb2927591dc0d7d17d6682e318e5c0c75610b35025bc75b2a847"},"schema_version":"1.0","source":{"id":"2506.02652","kind":"arxiv","version":1}},"canonical_sha256":"c2caaaa80d5fed2f346e5d183897d92e9b9ade9ad377f35a179e16ecb3d7da88","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c2caaaa80d5fed2f346e5d183897d92e9b9ade9ad377f35a179e16ecb3d7da88","first_computed_at":"2026-07-05T11:15:05.958862Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:15:05.958862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8dSNq3SiJb7HoWokfg0HEhAiwwTUASRhBI3nkbDTdGGOstpstF3lfjZNwZId2UIdGsHn+hjd/wuXN3q9PjdZBA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:15:05.959379Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.02652","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:16ae8776fa5f21f40c425f137c6cf498bd6294ce8d0cfe747552c81cd4021379","sha256:e7086341512ccdf439343f531a388039596d567435309b971501b695e24ca614"],"state_sha256":"14ade81712b5cc1fa7b57035ba415cf102b2b40f8f21326356e1ab2477956fd0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lu8KLsmZqog2lvaTRdpb7eTmLrZjMuzCRkbqizNClJf6yMLndrWbgpq1dIuErHpvkzIPnDZkTsHZ3daGNAlYBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T08:04:12.640218Z","bundle_sha256":"e5d9dc70958695f76c40ede5eb4e0d7bc9e25c18760b45e4e04842fa668e3411"}}