{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:RAKLH2B47UCIHM4NG7LBTLOK6S","short_pith_number":"pith:RAKLH2B4","canonical_record":{"source":{"id":"2606.27357","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-25T17:57:59Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"a041a1867e1c38e386e6132d7e9689df14e6a562ed838999b37d3b2bb5284019","abstract_canon_sha256":"2ed15c6517af6f481ceff843188ff345592c8af89b2009d1337eb4f7be26dd27"},"schema_version":"1.0"},"canonical_sha256":"8814b3e83cfd0483b38d37d619adcaf4b0563609d1ce2b57cd734882b2f34146","source":{"kind":"arxiv","id":"2606.27357","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.27357","created_at":"2026-06-26T01:16:19Z"},{"alias_kind":"arxiv_version","alias_value":"2606.27357v1","created_at":"2026-06-26T01:16:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.27357","created_at":"2026-06-26T01:16:19Z"},{"alias_kind":"pith_short_12","alias_value":"RAKLH2B47UCI","created_at":"2026-06-26T01:16:19Z"},{"alias_kind":"pith_short_16","alias_value":"RAKLH2B47UCIHM4N","created_at":"2026-06-26T01:16:19Z"},{"alias_kind":"pith_short_8","alias_value":"RAKLH2B4","created_at":"2026-06-26T01:16:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:RAKLH2B47UCIHM4NG7LBTLOK6S","target":"record","payload":{"canonical_record":{"source":{"id":"2606.27357","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-25T17:57:59Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"a041a1867e1c38e386e6132d7e9689df14e6a562ed838999b37d3b2bb5284019","abstract_canon_sha256":"2ed15c6517af6f481ceff843188ff345592c8af89b2009d1337eb4f7be26dd27"},"schema_version":"1.0"},"canonical_sha256":"8814b3e83cfd0483b38d37d619adcaf4b0563609d1ce2b57cd734882b2f34146","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-26T01:16:19.726782Z","signature_b64":"jgxbR094YsvgkghzFCFvw49/UqDDrUg+Zbz0vsiHEk1fxOa1kecwMhgP5XWhbrHxO5kic3y88FjTk2EPEZysDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8814b3e83cfd0483b38d37d619adcaf4b0563609d1ce2b57cd734882b2f34146","last_reissued_at":"2026-06-26T01:16:19.726275Z","signature_status":"signed_v1","first_computed_at":"2026-06-26T01:16:19.726275Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.27357","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":"2026-06-26T01:16:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GRZjiOfJ/oJ8xyVVblh2xb/lkjI1kQ/b0vb0tPqSzh3YiOlaL7RCNrdeNfpG5XzlNt0Ds4eHunKwz9A5y78OBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T09:36:14.554417Z"},"content_sha256":"88e8848d1768460a38c19c0b1c096b54b962b604ec0f9bbd03e69fab2eb4bc7a","schema_version":"1.0","event_id":"sha256:88e8848d1768460a38c19c0b1c096b54b962b604ec0f9bbd03e69fab2eb4bc7a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:RAKLH2B47UCIHM4NG7LBTLOK6S","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Typical distances in high-genus triangulations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Tanguy Lions","submitted_at":"2026-06-25T17:57:59Z","abstract_excerpt":"We study the distance between two uniformly chosen points on a uniform random triangulation whose genus g is proportional to the number of faces 2n. We show that the distance rescaled by log(n) converges in probability to a deterministic constant, which answers a conjecture of Budzinski, Chapuy and Louf. The proof relies on the precise study of the volume growth of the ball of radius r for r of order log(n). The main ingredients are the recent local convergence results for uniform triangulations with boundaries and the isoperimetric inequalities obtained by Budzinski and Louf."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.27357","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/2606.27357/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":"2026-06-26T01:16:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JgxTiqvfCc6myZJJG+fooP7ILj05G4/tJOAW2UsT34NLhKO1HuI2SwczB5u15xSTvd/FRGKi+dqL6JosyOG8Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T09:36:14.554889Z"},"content_sha256":"2ef412a097dac03f7d6e4e757d9ce39f8bc3d1cfec146c46e27b84216e7ab63f","schema_version":"1.0","event_id":"sha256:2ef412a097dac03f7d6e4e757d9ce39f8bc3d1cfec146c46e27b84216e7ab63f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RAKLH2B47UCIHM4NG7LBTLOK6S/bundle.json","state_url":"https://pith.science/pith/RAKLH2B47UCIHM4NG7LBTLOK6S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RAKLH2B47UCIHM4NG7LBTLOK6S/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":"2026-08-05T09:36:14Z","links":{"resolver":"https://pith.science/pith/RAKLH2B47UCIHM4NG7LBTLOK6S","bundle":"https://pith.science/pith/RAKLH2B47UCIHM4NG7LBTLOK6S/bundle.json","state":"https://pith.science/pith/RAKLH2B47UCIHM4NG7LBTLOK6S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RAKLH2B47UCIHM4NG7LBTLOK6S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:RAKLH2B47UCIHM4NG7LBTLOK6S","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":"2ed15c6517af6f481ceff843188ff345592c8af89b2009d1337eb4f7be26dd27","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-25T17:57:59Z","title_canon_sha256":"a041a1867e1c38e386e6132d7e9689df14e6a562ed838999b37d3b2bb5284019"},"schema_version":"1.0","source":{"id":"2606.27357","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.27357","created_at":"2026-06-26T01:16:19Z"},{"alias_kind":"arxiv_version","alias_value":"2606.27357v1","created_at":"2026-06-26T01:16:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.27357","created_at":"2026-06-26T01:16:19Z"},{"alias_kind":"pith_short_12","alias_value":"RAKLH2B47UCI","created_at":"2026-06-26T01:16:19Z"},{"alias_kind":"pith_short_16","alias_value":"RAKLH2B47UCIHM4N","created_at":"2026-06-26T01:16:19Z"},{"alias_kind":"pith_short_8","alias_value":"RAKLH2B4","created_at":"2026-06-26T01:16:19Z"}],"graph_snapshots":[{"event_id":"sha256:2ef412a097dac03f7d6e4e757d9ce39f8bc3d1cfec146c46e27b84216e7ab63f","target":"graph","created_at":"2026-06-26T01:16:19Z","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/2606.27357/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the distance between two uniformly chosen points on a uniform random triangulation whose genus g is proportional to the number of faces 2n. We show that the distance rescaled by log(n) converges in probability to a deterministic constant, which answers a conjecture of Budzinski, Chapuy and Louf. The proof relies on the precise study of the volume growth of the ball of radius r for r of order log(n). The main ingredients are the recent local convergence results for uniform triangulations with boundaries and the isoperimetric inequalities obtained by Budzinski and Louf.","authors_text":"Tanguy Lions","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-25T17:57:59Z","title":"Typical distances in high-genus triangulations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.27357","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":"sha256:88e8848d1768460a38c19c0b1c096b54b962b604ec0f9bbd03e69fab2eb4bc7a","target":"record","created_at":"2026-06-26T01:16:19Z","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":"2ed15c6517af6f481ceff843188ff345592c8af89b2009d1337eb4f7be26dd27","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-25T17:57:59Z","title_canon_sha256":"a041a1867e1c38e386e6132d7e9689df14e6a562ed838999b37d3b2bb5284019"},"schema_version":"1.0","source":{"id":"2606.27357","kind":"arxiv","version":1}},"canonical_sha256":"8814b3e83cfd0483b38d37d619adcaf4b0563609d1ce2b57cd734882b2f34146","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8814b3e83cfd0483b38d37d619adcaf4b0563609d1ce2b57cd734882b2f34146","first_computed_at":"2026-06-26T01:16:19.726275Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-26T01:16:19.726275Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jgxbR094YsvgkghzFCFvw49/UqDDrUg+Zbz0vsiHEk1fxOa1kecwMhgP5XWhbrHxO5kic3y88FjTk2EPEZysDg==","signature_status":"signed_v1","signed_at":"2026-06-26T01:16:19.726782Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.27357","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:88e8848d1768460a38c19c0b1c096b54b962b604ec0f9bbd03e69fab2eb4bc7a","sha256:2ef412a097dac03f7d6e4e757d9ce39f8bc3d1cfec146c46e27b84216e7ab63f"],"state_sha256":"f2ed933e3a384ebe0932632c30d39806abb2ac718e9d4b00dceef755db95f97b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YpBXoIUed2vmtiQBqjlIO7Ityl9PB77+otAB+mlFurCDnFJRgjOHVGy1o2bJX0q0w/85TPcclql8eCSN0z6IAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T09:36:14.559325Z","bundle_sha256":"2097724bb02e26193ddf883f8201b52c36cd39f32024df2b94050c093adf1f79"}}