{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:XQ4DQKJ6TVAXZ6ZCQEUS5D6ONW","short_pith_number":"pith:XQ4DQKJ6","canonical_record":{"source":{"id":"1802.05851","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-02-16T07:35:07Z","cross_cats_sorted":[],"title_canon_sha256":"ee9e72dd6812f207392edb10d8082defd245dc3ef29b260f10ce9fda85f0e0bb","abstract_canon_sha256":"8b6f1a020076d120d3febc7083c77214b98a3348320f5885f841cddb5e7dd82b"},"schema_version":"1.0"},"canonical_sha256":"bc3838293e9d417cfb2281292e8fce6dbd4385764423386c95035ea7f325342c","source":{"kind":"arxiv","id":"1802.05851","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.05851","created_at":"2026-05-18T00:21:34Z"},{"alias_kind":"arxiv_version","alias_value":"1802.05851v2","created_at":"2026-05-18T00:21:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.05851","created_at":"2026-05-18T00:21:34Z"},{"alias_kind":"pith_short_12","alias_value":"XQ4DQKJ6TVAX","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XQ4DQKJ6TVAXZ6ZC","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XQ4DQKJ6","created_at":"2026-05-18T12:33:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:XQ4DQKJ6TVAXZ6ZCQEUS5D6ONW","target":"record","payload":{"canonical_record":{"source":{"id":"1802.05851","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-02-16T07:35:07Z","cross_cats_sorted":[],"title_canon_sha256":"ee9e72dd6812f207392edb10d8082defd245dc3ef29b260f10ce9fda85f0e0bb","abstract_canon_sha256":"8b6f1a020076d120d3febc7083c77214b98a3348320f5885f841cddb5e7dd82b"},"schema_version":"1.0"},"canonical_sha256":"bc3838293e9d417cfb2281292e8fce6dbd4385764423386c95035ea7f325342c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:34.167678Z","signature_b64":"cbI5WPJSxwTj/+x1GoTUAHq4/0lvTyVaibhWaMZV9/MFolOuIjIUdw1+nKxRH+fUMsm7Yo9yYNEV2w81AfV+Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bc3838293e9d417cfb2281292e8fce6dbd4385764423386c95035ea7f325342c","last_reissued_at":"2026-05-18T00:21:34.167167Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:34.167167Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.05851","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":"2026-05-18T00:21:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jep78QbTLquH9mZ/tKNFQdWZqdXJJoUTTDoH1zpguoC6RkZEWMzWvy4mg+J9UvXUNMAEnc2a73cow+LnI/T9BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T21:36:19.830270Z"},"content_sha256":"3963366a23d94bc50abc0f032335ffc67c7b47728a620753a352bae37b12a75d","schema_version":"1.0","event_id":"sha256:3963366a23d94bc50abc0f032335ffc67c7b47728a620753a352bae37b12a75d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:XQ4DQKJ6TVAXZ6ZCQEUS5D6ONW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On triangle meshes with valence $6$ dominant vertices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jean-Marie Morvan","submitted_at":"2018-02-16T07:35:07Z","abstract_excerpt":"We study triangulations $\\cal T$ defined on a closed disc $X$ satisfying the following condition: In the interior of $X$, the valence of all vertices of $\\cal T$ except one of them (the irregular vertex) is $6$. By using a flat singular Riemannian metric adapted to $\\cal T$, we prove a uniqueness theorem when the valence of the irregular vertex is not a multiple of $6$. Moreover, for a given integer $k >1$, we exhibit non isomorphic triangulations on $X$ with the same boundary, and with a unique irregular vertex whose valence is $6k$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.05851","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":""},"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":"2026-05-18T00:21:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J1dMHUE3Oso/iMV6HmVsccNKDFf2mLrtREnU4n9PTxQeUPCFPI3M3PHbOEtW4i14LGy8SlRqeSOg4n4PqZksCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T21:36:19.830853Z"},"content_sha256":"a6efb7cbbe4646c60dc3a45f6b1c0128f3db0afd0aa1d7a08a2619b53b362468","schema_version":"1.0","event_id":"sha256:a6efb7cbbe4646c60dc3a45f6b1c0128f3db0afd0aa1d7a08a2619b53b362468"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XQ4DQKJ6TVAXZ6ZCQEUS5D6ONW/bundle.json","state_url":"https://pith.science/pith/XQ4DQKJ6TVAXZ6ZCQEUS5D6ONW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XQ4DQKJ6TVAXZ6ZCQEUS5D6ONW/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":"2026-06-06T21:36:19Z","links":{"resolver":"https://pith.science/pith/XQ4DQKJ6TVAXZ6ZCQEUS5D6ONW","bundle":"https://pith.science/pith/XQ4DQKJ6TVAXZ6ZCQEUS5D6ONW/bundle.json","state":"https://pith.science/pith/XQ4DQKJ6TVAXZ6ZCQEUS5D6ONW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XQ4DQKJ6TVAXZ6ZCQEUS5D6ONW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:XQ4DQKJ6TVAXZ6ZCQEUS5D6ONW","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":"8b6f1a020076d120d3febc7083c77214b98a3348320f5885f841cddb5e7dd82b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-02-16T07:35:07Z","title_canon_sha256":"ee9e72dd6812f207392edb10d8082defd245dc3ef29b260f10ce9fda85f0e0bb"},"schema_version":"1.0","source":{"id":"1802.05851","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.05851","created_at":"2026-05-18T00:21:34Z"},{"alias_kind":"arxiv_version","alias_value":"1802.05851v2","created_at":"2026-05-18T00:21:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.05851","created_at":"2026-05-18T00:21:34Z"},{"alias_kind":"pith_short_12","alias_value":"XQ4DQKJ6TVAX","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XQ4DQKJ6TVAXZ6ZC","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XQ4DQKJ6","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:a6efb7cbbe4646c60dc3a45f6b1c0128f3db0afd0aa1d7a08a2619b53b362468","target":"graph","created_at":"2026-05-18T00:21:34Z","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"},"paper":{"abstract_excerpt":"We study triangulations $\\cal T$ defined on a closed disc $X$ satisfying the following condition: In the interior of $X$, the valence of all vertices of $\\cal T$ except one of them (the irregular vertex) is $6$. By using a flat singular Riemannian metric adapted to $\\cal T$, we prove a uniqueness theorem when the valence of the irregular vertex is not a multiple of $6$. Moreover, for a given integer $k >1$, we exhibit non isomorphic triangulations on $X$ with the same boundary, and with a unique irregular vertex whose valence is $6k$.","authors_text":"Jean-Marie Morvan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-02-16T07:35:07Z","title":"On triangle meshes with valence $6$ dominant vertices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.05851","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":"sha256:3963366a23d94bc50abc0f032335ffc67c7b47728a620753a352bae37b12a75d","target":"record","created_at":"2026-05-18T00:21:34Z","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":"8b6f1a020076d120d3febc7083c77214b98a3348320f5885f841cddb5e7dd82b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-02-16T07:35:07Z","title_canon_sha256":"ee9e72dd6812f207392edb10d8082defd245dc3ef29b260f10ce9fda85f0e0bb"},"schema_version":"1.0","source":{"id":"1802.05851","kind":"arxiv","version":2}},"canonical_sha256":"bc3838293e9d417cfb2281292e8fce6dbd4385764423386c95035ea7f325342c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bc3838293e9d417cfb2281292e8fce6dbd4385764423386c95035ea7f325342c","first_computed_at":"2026-05-18T00:21:34.167167Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:21:34.167167Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cbI5WPJSxwTj/+x1GoTUAHq4/0lvTyVaibhWaMZV9/MFolOuIjIUdw1+nKxRH+fUMsm7Yo9yYNEV2w81AfV+Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:21:34.167678Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.05851","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3963366a23d94bc50abc0f032335ffc67c7b47728a620753a352bae37b12a75d","sha256:a6efb7cbbe4646c60dc3a45f6b1c0128f3db0afd0aa1d7a08a2619b53b362468"],"state_sha256":"737e1428d4171275a0ee03c61629718c21ba0d668c1fc2901b07e9fdb77a2bf0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qBMyrTGMMTH4+/ELPNKIHfRqjWQwT6oy02FeUyig4+gZSFgkQmgvz5iOy0KFsU3Vr/JAsfN9kHNx1sMPmb8/AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T21:36:19.833930Z","bundle_sha256":"05cffe74b01bac60712745ff8b3b02c92689c5abd3b496e1c4a2954b4d144f67"}}