{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:AXFRT5B3K3DMTYDMG2OJMJPUY2","short_pith_number":"pith:AXFRT5B3","canonical_record":{"source":{"id":"2211.07464","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.GT","submitted_at":"2022-11-14T15:45:40Z","cross_cats_sorted":[],"title_canon_sha256":"939fa606380f15a099d9f2578ebe9618c8a62b99f29f35169e9a2f350224b675","abstract_canon_sha256":"e68c2284de0829c4d0cdd63cabe434cffc7e80bacbf3c927924e8d2e1b2d4eb7"},"schema_version":"1.0"},"canonical_sha256":"05cb19f43b56c6c9e06c369c9625f4c6b4824a49a34b3fe25253c57dbbc8dbba","source":{"kind":"arxiv","id":"2211.07464","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.07464","created_at":"2026-07-05T11:43:04Z"},{"alias_kind":"arxiv_version","alias_value":"2211.07464v2","created_at":"2026-07-05T11:43:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.07464","created_at":"2026-07-05T11:43:04Z"},{"alias_kind":"pith_short_12","alias_value":"AXFRT5B3K3DM","created_at":"2026-07-05T11:43:04Z"},{"alias_kind":"pith_short_16","alias_value":"AXFRT5B3K3DMTYDM","created_at":"2026-07-05T11:43:04Z"},{"alias_kind":"pith_short_8","alias_value":"AXFRT5B3","created_at":"2026-07-05T11:43:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:AXFRT5B3K3DMTYDMG2OJMJPUY2","target":"record","payload":{"canonical_record":{"source":{"id":"2211.07464","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.GT","submitted_at":"2022-11-14T15:45:40Z","cross_cats_sorted":[],"title_canon_sha256":"939fa606380f15a099d9f2578ebe9618c8a62b99f29f35169e9a2f350224b675","abstract_canon_sha256":"e68c2284de0829c4d0cdd63cabe434cffc7e80bacbf3c927924e8d2e1b2d4eb7"},"schema_version":"1.0"},"canonical_sha256":"05cb19f43b56c6c9e06c369c9625f4c6b4824a49a34b3fe25253c57dbbc8dbba","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:43:04.734124Z","signature_b64":"PNfpCM4ChshChstQSqvmEkFkEDEZWJLUq8zbKDfNG1Olxxle/cDT8LYth2q+KREqTTDg4k/0Spfrh4L3GbBXAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"05cb19f43b56c6c9e06c369c9625f4c6b4824a49a34b3fe25253c57dbbc8dbba","last_reissued_at":"2026-07-05T11:43:04.733715Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:43:04.733715Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2211.07464","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":"2026-07-05T11:43:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0B4poKraKoYXo64a2PxFF+K+1sra5Cb3CH75Cqx0MtVMOKhES0jKKq3vKfhF4ESsTGCER1oO7yoKDzJfJxU7AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T04:59:17.278264Z"},"content_sha256":"a6712ea321bf60ab1dc4a6c0c1e58321dd442163d54f6209e294f1a555db09ab","schema_version":"1.0","event_id":"sha256:a6712ea321bf60ab1dc4a6c0c1e58321dd442163d54f6209e294f1a555db09ab"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:AXFRT5B3K3DMTYDMG2OJMJPUY2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rigidity of infinite inversive distance circle packings in the plane","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Siqi Zhang, Xu Xu, Yanwen Luo","submitted_at":"2022-11-14T15:45:40Z","abstract_excerpt":"In 2004, Bowers-Stephenson [2] introduced the inversive distance circle packings as a natural generalization of Thurston's circle packings. They further conjectured the rigidity of infinite inversive distance circle packings in the plane. Motivated by the recent work of Luo-Sun-Wu [22] on Luo's vertex scaling, we prove Bower-Stephenson's conjecture for inversive distance circle packings in the hexagonal triangulated plane. This generalizes Rodin-Sullivan's famous result [13] on the rigidity of infinite tangential circle packings in the hexagonal triangulated plane. The key tools include a maxi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.07464","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/2211.07464/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":"2026-07-05T11:43:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9vNVG4BDb2jL9TnHoDgxuFEOnXvu4dYq3vXfEhLbxgAwX+Uy5C+cFtr8UN9io8BB9XWxahnOzbSgE7vSMj0DCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T04:59:17.278674Z"},"content_sha256":"fe179294a6bcdfc717b0e8216f8ba5dc28784a766ceab9f3a768cd64204c2c9b","schema_version":"1.0","event_id":"sha256:fe179294a6bcdfc717b0e8216f8ba5dc28784a766ceab9f3a768cd64204c2c9b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AXFRT5B3K3DMTYDMG2OJMJPUY2/bundle.json","state_url":"https://pith.science/pith/AXFRT5B3K3DMTYDMG2OJMJPUY2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AXFRT5B3K3DMTYDMG2OJMJPUY2/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":"2026-07-07T04:59:17Z","links":{"resolver":"https://pith.science/pith/AXFRT5B3K3DMTYDMG2OJMJPUY2","bundle":"https://pith.science/pith/AXFRT5B3K3DMTYDMG2OJMJPUY2/bundle.json","state":"https://pith.science/pith/AXFRT5B3K3DMTYDMG2OJMJPUY2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AXFRT5B3K3DMTYDMG2OJMJPUY2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:AXFRT5B3K3DMTYDMG2OJMJPUY2","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":"e68c2284de0829c4d0cdd63cabe434cffc7e80bacbf3c927924e8d2e1b2d4eb7","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.GT","submitted_at":"2022-11-14T15:45:40Z","title_canon_sha256":"939fa606380f15a099d9f2578ebe9618c8a62b99f29f35169e9a2f350224b675"},"schema_version":"1.0","source":{"id":"2211.07464","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.07464","created_at":"2026-07-05T11:43:04Z"},{"alias_kind":"arxiv_version","alias_value":"2211.07464v2","created_at":"2026-07-05T11:43:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.07464","created_at":"2026-07-05T11:43:04Z"},{"alias_kind":"pith_short_12","alias_value":"AXFRT5B3K3DM","created_at":"2026-07-05T11:43:04Z"},{"alias_kind":"pith_short_16","alias_value":"AXFRT5B3K3DMTYDM","created_at":"2026-07-05T11:43:04Z"},{"alias_kind":"pith_short_8","alias_value":"AXFRT5B3","created_at":"2026-07-05T11:43:04Z"}],"graph_snapshots":[{"event_id":"sha256:fe179294a6bcdfc717b0e8216f8ba5dc28784a766ceab9f3a768cd64204c2c9b","target":"graph","created_at":"2026-07-05T11:43:04Z","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/2211.07464/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In 2004, Bowers-Stephenson [2] introduced the inversive distance circle packings as a natural generalization of Thurston's circle packings. They further conjectured the rigidity of infinite inversive distance circle packings in the plane. Motivated by the recent work of Luo-Sun-Wu [22] on Luo's vertex scaling, we prove Bower-Stephenson's conjecture for inversive distance circle packings in the hexagonal triangulated plane. This generalizes Rodin-Sullivan's famous result [13] on the rigidity of infinite tangential circle packings in the hexagonal triangulated plane. The key tools include a maxi","authors_text":"Siqi Zhang, Xu Xu, Yanwen Luo","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.GT","submitted_at":"2022-11-14T15:45:40Z","title":"Rigidity of infinite inversive distance circle packings in the plane"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.07464","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:a6712ea321bf60ab1dc4a6c0c1e58321dd442163d54f6209e294f1a555db09ab","target":"record","created_at":"2026-07-05T11:43:04Z","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":"e68c2284de0829c4d0cdd63cabe434cffc7e80bacbf3c927924e8d2e1b2d4eb7","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.GT","submitted_at":"2022-11-14T15:45:40Z","title_canon_sha256":"939fa606380f15a099d9f2578ebe9618c8a62b99f29f35169e9a2f350224b675"},"schema_version":"1.0","source":{"id":"2211.07464","kind":"arxiv","version":2}},"canonical_sha256":"05cb19f43b56c6c9e06c369c9625f4c6b4824a49a34b3fe25253c57dbbc8dbba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"05cb19f43b56c6c9e06c369c9625f4c6b4824a49a34b3fe25253c57dbbc8dbba","first_computed_at":"2026-07-05T11:43:04.733715Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:43:04.733715Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PNfpCM4ChshChstQSqvmEkFkEDEZWJLUq8zbKDfNG1Olxxle/cDT8LYth2q+KREqTTDg4k/0Spfrh4L3GbBXAg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:43:04.734124Z","signed_message":"canonical_sha256_bytes"},"source_id":"2211.07464","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a6712ea321bf60ab1dc4a6c0c1e58321dd442163d54f6209e294f1a555db09ab","sha256:fe179294a6bcdfc717b0e8216f8ba5dc28784a766ceab9f3a768cd64204c2c9b"],"state_sha256":"5410cde32fbb40580f677ce42465532e930cbdca00f1dbfd4f6bbd3aaff14f3f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QBC5GlYOD9pJjjYs0hv4X2T5TAg+tE6iYpjS5gxAYp5MkUE2hYDZUMS96ctpmR0QaIpKxQNE9vMu9zgfuPhfAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T04:59:17.281276Z","bundle_sha256":"bbef163ad4cf7e822c12f5f345e558e2333f2c222ac6e225ecf0669215f18d67"}}