{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:SN5MMT3TRON3HHR25N5T3ZMRM7","short_pith_number":"pith:SN5MMT3T","canonical_record":{"source":{"id":"2402.07509","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-02-12T09:30:44Z","cross_cats_sorted":[],"title_canon_sha256":"194e341ef002e1d54a18190424f03e3ddb0988cda0a9586668f3397d37556161","abstract_canon_sha256":"dc8b20989282db2c6be7b534d40b8073a323a51bf72b154bb584dc1fc0a0d076"},"schema_version":"1.0"},"canonical_sha256":"937ac64f738b9bb39e3aeb7b3de59167d0cf2aa538b4911f76c04c0f81e2f197","source":{"kind":"arxiv","id":"2402.07509","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.07509","created_at":"2026-07-05T10:11:57Z"},{"alias_kind":"arxiv_version","alias_value":"2402.07509v2","created_at":"2026-07-05T10:11:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.07509","created_at":"2026-07-05T10:11:57Z"},{"alias_kind":"pith_short_12","alias_value":"SN5MMT3TRON3","created_at":"2026-07-05T10:11:57Z"},{"alias_kind":"pith_short_16","alias_value":"SN5MMT3TRON3HHR2","created_at":"2026-07-05T10:11:57Z"},{"alias_kind":"pith_short_8","alias_value":"SN5MMT3T","created_at":"2026-07-05T10:11:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:SN5MMT3TRON3HHR25N5T3ZMRM7","target":"record","payload":{"canonical_record":{"source":{"id":"2402.07509","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-02-12T09:30:44Z","cross_cats_sorted":[],"title_canon_sha256":"194e341ef002e1d54a18190424f03e3ddb0988cda0a9586668f3397d37556161","abstract_canon_sha256":"dc8b20989282db2c6be7b534d40b8073a323a51bf72b154bb584dc1fc0a0d076"},"schema_version":"1.0"},"canonical_sha256":"937ac64f738b9bb39e3aeb7b3de59167d0cf2aa538b4911f76c04c0f81e2f197","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:11:57.804405Z","signature_b64":"W/mIPEaEaz/gyNVqms0tLqjR4U6fnJjgp/cmX5QJxH0jaNpVCYK5CMptjIclbCFAaX8ESjR+HexiOz63ACr6Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"937ac64f738b9bb39e3aeb7b3de59167d0cf2aa538b4911f76c04c0f81e2f197","last_reissued_at":"2026-07-05T10:11:57.803891Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:11:57.803891Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2402.07509","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:11:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wu+6lzFHvA9kZ5ydAJJ81oZY3kOYvtepGVuU7QXsmEfOfglVEa7hvcqg/lyCW4ndQdibh3N3TB9qvgqpt1kbAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T01:56:39.756518Z"},"content_sha256":"a0987796a8a6a923ae0d5c01f8a2b9e7a0e1e126231687bc5693b97df4e189a3","schema_version":"1.0","event_id":"sha256:a0987796a8a6a923ae0d5c01f8a2b9e7a0e1e126231687bc5693b97df4e189a3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:SN5MMT3TRON3HHR25N5T3ZMRM7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"First-order behavior of the time constant in non-isotropic continuous first-passage percolation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Anne-Laure Basdevant (LPSM), Jean-Baptiste Gou\\'er\\'e (IDP), Marie Th\\'eret (FP2M, Modal'x)","submitted_at":"2024-02-12T09:30:44Z","abstract_excerpt":"Consider $\\Xi$ a homogeneous Poisson point process on $\\mathbb{R}^d$ ($d\\geq 2$) with unit intensity  with respect to the Lebesgue measure. For $\\varepsilon\\geq 0$,  we define the Boolean model $\\Sigma_{p, \\varepsilon}$ as the union of the balls of volume $\\varepsilon$ for the $p$-norm ($p\\in [1,\\infty]$) and centered at the points of $\\Xi$. We define a random pseudo-metric on $\\mathbb{R}^d$ by associating with any path a travel time equal to its $p$-length outside $\\Sigma_{p,\\varepsilon}$. This defines a continuous model of first-passage percolation, that has been studied in \\cite{GT17,GT22} "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.07509","kind":"arxiv","version":2},"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/2402.07509/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":"2026-07-05T10:11:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h7MebZAXnLZvQQaQMTXHbWXKwBU+4ZiCBnnHHxkEBvU3jd0yXixrP5HHJUN97AMeKzabaio3UWv3ux3cmjUJCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T01:56:39.757496Z"},"content_sha256":"b2ca18557495f584e359827d13f3f39ff1cf200912adb6915432ac1c7ea15f71","schema_version":"1.0","event_id":"sha256:b2ca18557495f584e359827d13f3f39ff1cf200912adb6915432ac1c7ea15f71"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SN5MMT3TRON3HHR25N5T3ZMRM7/bundle.json","state_url":"https://pith.science/pith/SN5MMT3TRON3HHR25N5T3ZMRM7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SN5MMT3TRON3HHR25N5T3ZMRM7/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":"2026-08-06T01:56:39Z","links":{"resolver":"https://pith.science/pith/SN5MMT3TRON3HHR25N5T3ZMRM7","bundle":"https://pith.science/pith/SN5MMT3TRON3HHR25N5T3ZMRM7/bundle.json","state":"https://pith.science/pith/SN5MMT3TRON3HHR25N5T3ZMRM7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SN5MMT3TRON3HHR25N5T3ZMRM7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:SN5MMT3TRON3HHR25N5T3ZMRM7","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":"dc8b20989282db2c6be7b534d40b8073a323a51bf72b154bb584dc1fc0a0d076","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-02-12T09:30:44Z","title_canon_sha256":"194e341ef002e1d54a18190424f03e3ddb0988cda0a9586668f3397d37556161"},"schema_version":"1.0","source":{"id":"2402.07509","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.07509","created_at":"2026-07-05T10:11:57Z"},{"alias_kind":"arxiv_version","alias_value":"2402.07509v2","created_at":"2026-07-05T10:11:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.07509","created_at":"2026-07-05T10:11:57Z"},{"alias_kind":"pith_short_12","alias_value":"SN5MMT3TRON3","created_at":"2026-07-05T10:11:57Z"},{"alias_kind":"pith_short_16","alias_value":"SN5MMT3TRON3HHR2","created_at":"2026-07-05T10:11:57Z"},{"alias_kind":"pith_short_8","alias_value":"SN5MMT3T","created_at":"2026-07-05T10:11:57Z"}],"graph_snapshots":[{"event_id":"sha256:b2ca18557495f584e359827d13f3f39ff1cf200912adb6915432ac1c7ea15f71","target":"graph","created_at":"2026-07-05T10:11:57Z","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/2402.07509/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Consider $\\Xi$ a homogeneous Poisson point process on $\\mathbb{R}^d$ ($d\\geq 2$) with unit intensity  with respect to the Lebesgue measure. For $\\varepsilon\\geq 0$,  we define the Boolean model $\\Sigma_{p, \\varepsilon}$ as the union of the balls of volume $\\varepsilon$ for the $p$-norm ($p\\in [1,\\infty]$) and centered at the points of $\\Xi$. We define a random pseudo-metric on $\\mathbb{R}^d$ by associating with any path a travel time equal to its $p$-length outside $\\Sigma_{p,\\varepsilon}$. This defines a continuous model of first-passage percolation, that has been studied in \\cite{GT17,GT22} ","authors_text":"Anne-Laure Basdevant (LPSM), Jean-Baptiste Gou\\'er\\'e (IDP), Marie Th\\'eret (FP2M, Modal'x)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-02-12T09:30:44Z","title":"First-order behavior of the time constant in non-isotropic continuous first-passage percolation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.07509","kind":"arxiv","version":2},"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:a0987796a8a6a923ae0d5c01f8a2b9e7a0e1e126231687bc5693b97df4e189a3","target":"record","created_at":"2026-07-05T10:11:57Z","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":"dc8b20989282db2c6be7b534d40b8073a323a51bf72b154bb584dc1fc0a0d076","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-02-12T09:30:44Z","title_canon_sha256":"194e341ef002e1d54a18190424f03e3ddb0988cda0a9586668f3397d37556161"},"schema_version":"1.0","source":{"id":"2402.07509","kind":"arxiv","version":2}},"canonical_sha256":"937ac64f738b9bb39e3aeb7b3de59167d0cf2aa538b4911f76c04c0f81e2f197","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"937ac64f738b9bb39e3aeb7b3de59167d0cf2aa538b4911f76c04c0f81e2f197","first_computed_at":"2026-07-05T10:11:57.803891Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:11:57.803891Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W/mIPEaEaz/gyNVqms0tLqjR4U6fnJjgp/cmX5QJxH0jaNpVCYK5CMptjIclbCFAaX8ESjR+HexiOz63ACr6Ag==","signature_status":"signed_v1","signed_at":"2026-07-05T10:11:57.804405Z","signed_message":"canonical_sha256_bytes"},"source_id":"2402.07509","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a0987796a8a6a923ae0d5c01f8a2b9e7a0e1e126231687bc5693b97df4e189a3","sha256:b2ca18557495f584e359827d13f3f39ff1cf200912adb6915432ac1c7ea15f71"],"state_sha256":"06aee6ba8b2de0005c58584c86a02059ac407cdd25e6959b8b2ee8ee5121acd1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aDCyCFrHVm1bM9/TPilnvSxs1yKfmyPKSGvDNYHG5vig8XX/hNj55oZObcEL/T5jXDmLSqBdxoURddMuNmBiAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T01:56:39.770250Z","bundle_sha256":"c284bbddad1a95919ae18b6088cd2ae5fbce2bff38a208912393791f2c9098f1"}}