{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:YG3WUDTWHFOVLKUJK4IFY56QU5","short_pith_number":"pith:YG3WUDTW","canonical_record":{"source":{"id":"1310.8398","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-10-31T06:39:31Z","cross_cats_sorted":["math.GT","math.MG"],"title_canon_sha256":"bf7d32cff9e8acaf60464780b0db039ba298fddc99ce86c9eebb6569b4686101","abstract_canon_sha256":"c3d5ed501c895d15b86a509ddf1b6e68690c4a8b2f735ac729a67fcff022db2f"},"schema_version":"1.0"},"canonical_sha256":"c1b76a0e76395d55aa8957105c77d0a75552159516189f46cd7853abff1e5ef0","source":{"kind":"arxiv","id":"1310.8398","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.8398","created_at":"2026-05-18T03:08:17Z"},{"alias_kind":"arxiv_version","alias_value":"1310.8398v1","created_at":"2026-05-18T03:08:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.8398","created_at":"2026-05-18T03:08:17Z"},{"alias_kind":"pith_short_12","alias_value":"YG3WUDTWHFOV","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"YG3WUDTWHFOVLKUJ","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"YG3WUDTW","created_at":"2026-05-18T12:28:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:YG3WUDTWHFOVLKUJK4IFY56QU5","target":"record","payload":{"canonical_record":{"source":{"id":"1310.8398","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-10-31T06:39:31Z","cross_cats_sorted":["math.GT","math.MG"],"title_canon_sha256":"bf7d32cff9e8acaf60464780b0db039ba298fddc99ce86c9eebb6569b4686101","abstract_canon_sha256":"c3d5ed501c895d15b86a509ddf1b6e68690c4a8b2f735ac729a67fcff022db2f"},"schema_version":"1.0"},"canonical_sha256":"c1b76a0e76395d55aa8957105c77d0a75552159516189f46cd7853abff1e5ef0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:08:17.183521Z","signature_b64":"woqpkOiJs0+Jgk72nlzHKbIM18p8jVPYKPMojwvklBteZr9rzxSgnJC6EmCKgVsKITZFJLF19OB//7YAsV+cBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c1b76a0e76395d55aa8957105c77d0a75552159516189f46cd7853abff1e5ef0","last_reissued_at":"2026-05-18T03:08:17.182960Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:08:17.182960Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.8398","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":"2026-05-18T03:08:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e/Xd9uiskZKN1Q3DNk77ARGfAj0KuNwPu9NltDbj69LdBDJ/+tcxtqGEEvK82iEUvV6sFZuwhJcUVZu1y5BeBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T20:08:18.740440Z"},"content_sha256":"6fa0aa7b32615767e7e2f984f2ae2418cf2eea128bb5d87a071ef97fdf5a2007","schema_version":"1.0","event_id":"sha256:6fa0aa7b32615767e7e2f984f2ae2418cf2eea128bb5d87a071ef97fdf5a2007"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:YG3WUDTWHFOVLKUJK4IFY56QU5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Weak Minkowski Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT","math.MG"],"primary_cat":"math.DG","authors_text":"Athanase Papadopoulos (IRMA), Marc Troyanov","submitted_at":"2013-10-31T06:39:31Z","abstract_excerpt":"We define the notion of weak Minkowski metric and prove some basic properties of such metrics. We also highlight some of the important analogies between Minkowski geometry and the Funk and Hilbert geometries."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.8398","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":""},"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":"2026-05-18T03:08:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gbQj0GfAPbA1qYTdf5Fzm+GnacCMOITWbWjsoFyx7KGwi1/YxUW2fFcY9lxhqHMGN+UYdK0z7YdQroEDYU03Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T20:08:18.740793Z"},"content_sha256":"0096bbbafaebb909ea7f89004fc8ba9b3cb77545d11433391d2f24bdba1d0ede","schema_version":"1.0","event_id":"sha256:0096bbbafaebb909ea7f89004fc8ba9b3cb77545d11433391d2f24bdba1d0ede"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YG3WUDTWHFOVLKUJK4IFY56QU5/bundle.json","state_url":"https://pith.science/pith/YG3WUDTWHFOVLKUJK4IFY56QU5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YG3WUDTWHFOVLKUJK4IFY56QU5/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":"2026-06-01T20:08:18Z","links":{"resolver":"https://pith.science/pith/YG3WUDTWHFOVLKUJK4IFY56QU5","bundle":"https://pith.science/pith/YG3WUDTWHFOVLKUJK4IFY56QU5/bundle.json","state":"https://pith.science/pith/YG3WUDTWHFOVLKUJK4IFY56QU5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YG3WUDTWHFOVLKUJK4IFY56QU5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:YG3WUDTWHFOVLKUJK4IFY56QU5","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":"c3d5ed501c895d15b86a509ddf1b6e68690c4a8b2f735ac729a67fcff022db2f","cross_cats_sorted":["math.GT","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-10-31T06:39:31Z","title_canon_sha256":"bf7d32cff9e8acaf60464780b0db039ba298fddc99ce86c9eebb6569b4686101"},"schema_version":"1.0","source":{"id":"1310.8398","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.8398","created_at":"2026-05-18T03:08:17Z"},{"alias_kind":"arxiv_version","alias_value":"1310.8398v1","created_at":"2026-05-18T03:08:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.8398","created_at":"2026-05-18T03:08:17Z"},{"alias_kind":"pith_short_12","alias_value":"YG3WUDTWHFOV","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"YG3WUDTWHFOVLKUJ","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"YG3WUDTW","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:0096bbbafaebb909ea7f89004fc8ba9b3cb77545d11433391d2f24bdba1d0ede","target":"graph","created_at":"2026-05-18T03:08:17Z","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 define the notion of weak Minkowski metric and prove some basic properties of such metrics. We also highlight some of the important analogies between Minkowski geometry and the Funk and Hilbert geometries.","authors_text":"Athanase Papadopoulos (IRMA), Marc Troyanov","cross_cats":["math.GT","math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-10-31T06:39:31Z","title":"Weak Minkowski Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.8398","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":"sha256:6fa0aa7b32615767e7e2f984f2ae2418cf2eea128bb5d87a071ef97fdf5a2007","target":"record","created_at":"2026-05-18T03:08:17Z","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":"c3d5ed501c895d15b86a509ddf1b6e68690c4a8b2f735ac729a67fcff022db2f","cross_cats_sorted":["math.GT","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-10-31T06:39:31Z","title_canon_sha256":"bf7d32cff9e8acaf60464780b0db039ba298fddc99ce86c9eebb6569b4686101"},"schema_version":"1.0","source":{"id":"1310.8398","kind":"arxiv","version":1}},"canonical_sha256":"c1b76a0e76395d55aa8957105c77d0a75552159516189f46cd7853abff1e5ef0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c1b76a0e76395d55aa8957105c77d0a75552159516189f46cd7853abff1e5ef0","first_computed_at":"2026-05-18T03:08:17.182960Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:08:17.182960Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"woqpkOiJs0+Jgk72nlzHKbIM18p8jVPYKPMojwvklBteZr9rzxSgnJC6EmCKgVsKITZFJLF19OB//7YAsV+cBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:08:17.183521Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.8398","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6fa0aa7b32615767e7e2f984f2ae2418cf2eea128bb5d87a071ef97fdf5a2007","sha256:0096bbbafaebb909ea7f89004fc8ba9b3cb77545d11433391d2f24bdba1d0ede"],"state_sha256":"1bf21b07e310e3ea85947265ea867f487da34787cfd348f903c687c8cc95d9ae"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z542qxUHmwB5Hq6dXw/ZU9PPVN6G9dmjbRQUUqsfSUY/pXEnI0tAHWSyywiuje4bBvTXHIAe5MHujpZzcfu1Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T20:08:18.742790Z","bundle_sha256":"1bd1a28b6c9131ece8f269661d028c75c2fb4750c585fd7b3a8c4f2b3e8ed882"}}