{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2001:VM5M5PPFYS7TSK4B7L5RSVXQHK","short_pith_number":"pith:VM5M5PPF","canonical_record":{"source":{"id":"math/0104064","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2001-04-05T15:36:46Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"a227cce270865556870f0be0a228f2ae7d995c9357f6f52c32e027d4fd2bcade","abstract_canon_sha256":"5fc4901beb33998d944cef6828a9deac15e716f237f87e3e393cb27ac00e14d4"},"schema_version":"1.0"},"canonical_sha256":"ab3acebde5c4bf392b81fafb1956f03a8d431943cf1c3b9e8f172d425334f83d","source":{"kind":"arxiv","id":"math/0104064","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0104064","created_at":"2026-07-04T14:35:09Z"},{"alias_kind":"arxiv_version","alias_value":"math/0104064v1","created_at":"2026-07-04T14:35:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0104064","created_at":"2026-07-04T14:35:09Z"},{"alias_kind":"pith_short_12","alias_value":"VM5M5PPFYS7T","created_at":"2026-07-04T14:35:09Z"},{"alias_kind":"pith_short_16","alias_value":"VM5M5PPFYS7TSK4B","created_at":"2026-07-04T14:35:09Z"},{"alias_kind":"pith_short_8","alias_value":"VM5M5PPF","created_at":"2026-07-04T14:35:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2001:VM5M5PPFYS7TSK4B7L5RSVXQHK","target":"record","payload":{"canonical_record":{"source":{"id":"math/0104064","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2001-04-05T15:36:46Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"a227cce270865556870f0be0a228f2ae7d995c9357f6f52c32e027d4fd2bcade","abstract_canon_sha256":"5fc4901beb33998d944cef6828a9deac15e716f237f87e3e393cb27ac00e14d4"},"schema_version":"1.0"},"canonical_sha256":"ab3acebde5c4bf392b81fafb1956f03a8d431943cf1c3b9e8f172d425334f83d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:35:09.350804Z","signature_b64":"yXMhUjvs+ERR6FVLA1dWnEVSJRPWwV0nX/j0y/baC0S/rcBTU3wVoFfhSQ0PUHHHU75ky7KmrhsNjEqzV5yGBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ab3acebde5c4bf392b81fafb1956f03a8d431943cf1c3b9e8f172d425334f83d","last_reissued_at":"2026-07-04T14:35:09.350477Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:35:09.350477Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0104064","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":"2026-07-04T14:35:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JuZ8JvBD70MVPH9h/i7sx6xQ2sfa1gYyhFLjCmL67KKmlfriLE65bEE1pKVDYsPi078K49BS+X+saBXpnEBFBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T11:43:39.759248Z"},"content_sha256":"4eb0ea3e15e49292d77625a3514c96e1898dab2dc6a402eb631ec245a4102cbd","schema_version":"1.0","event_id":"sha256:4eb0ea3e15e49292d77625a3514c96e1898dab2dc6a402eb631ec245a4102cbd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2001:VM5M5PPFYS7TSK4B7L5RSVXQHK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Compact Polygons","license":"","headline":"","cross_cats":["math.GT"],"primary_cat":"math.DG","authors_text":"Linus Kramer","submitted_at":"2001-04-05T15:36:46Z","abstract_excerpt":"We develop the basic topological properties of compact polygons, i.e. of compact topological Tits buildings of rank two. It is proved that the Coxeter diagram of such a building is always crystallographic, that is, compact connected n-gons exist only for n=3,4,6. We classify compact polygons which admit a transitive group action, showing that such a polygon is Moufang and thus related to a real Lie group of rank 2."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0104064","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/math/0104064/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":"2026-07-04T14:35:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Knd7GPVpfseK/JY9Rddxr9smOJWW7ZbzHOfsYcH5uoM/V93T9CFhINRP19uwjxIiuB+4KPw9wZ67TuDv/P4CDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T11:43:39.759644Z"},"content_sha256":"711b7fcb515ab315c9344734fe76716188e6168c2a223be4e076b4f9eb323d57","schema_version":"1.0","event_id":"sha256:711b7fcb515ab315c9344734fe76716188e6168c2a223be4e076b4f9eb323d57"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VM5M5PPFYS7TSK4B7L5RSVXQHK/bundle.json","state_url":"https://pith.science/pith/VM5M5PPFYS7TSK4B7L5RSVXQHK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VM5M5PPFYS7TSK4B7L5RSVXQHK/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":"2026-07-07T11:43:39Z","links":{"resolver":"https://pith.science/pith/VM5M5PPFYS7TSK4B7L5RSVXQHK","bundle":"https://pith.science/pith/VM5M5PPFYS7TSK4B7L5RSVXQHK/bundle.json","state":"https://pith.science/pith/VM5M5PPFYS7TSK4B7L5RSVXQHK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VM5M5PPFYS7TSK4B7L5RSVXQHK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:VM5M5PPFYS7TSK4B7L5RSVXQHK","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":"5fc4901beb33998d944cef6828a9deac15e716f237f87e3e393cb27ac00e14d4","cross_cats_sorted":["math.GT"],"license":"","primary_cat":"math.DG","submitted_at":"2001-04-05T15:36:46Z","title_canon_sha256":"a227cce270865556870f0be0a228f2ae7d995c9357f6f52c32e027d4fd2bcade"},"schema_version":"1.0","source":{"id":"math/0104064","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0104064","created_at":"2026-07-04T14:35:09Z"},{"alias_kind":"arxiv_version","alias_value":"math/0104064v1","created_at":"2026-07-04T14:35:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0104064","created_at":"2026-07-04T14:35:09Z"},{"alias_kind":"pith_short_12","alias_value":"VM5M5PPFYS7T","created_at":"2026-07-04T14:35:09Z"},{"alias_kind":"pith_short_16","alias_value":"VM5M5PPFYS7TSK4B","created_at":"2026-07-04T14:35:09Z"},{"alias_kind":"pith_short_8","alias_value":"VM5M5PPF","created_at":"2026-07-04T14:35:09Z"}],"graph_snapshots":[{"event_id":"sha256:711b7fcb515ab315c9344734fe76716188e6168c2a223be4e076b4f9eb323d57","target":"graph","created_at":"2026-07-04T14:35:09Z","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/math/0104064/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We develop the basic topological properties of compact polygons, i.e. of compact topological Tits buildings of rank two. It is proved that the Coxeter diagram of such a building is always crystallographic, that is, compact connected n-gons exist only for n=3,4,6. We classify compact polygons which admit a transitive group action, showing that such a polygon is Moufang and thus related to a real Lie group of rank 2.","authors_text":"Linus Kramer","cross_cats":["math.GT"],"headline":"","license":"","primary_cat":"math.DG","submitted_at":"2001-04-05T15:36:46Z","title":"Compact Polygons"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0104064","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":"sha256:4eb0ea3e15e49292d77625a3514c96e1898dab2dc6a402eb631ec245a4102cbd","target":"record","created_at":"2026-07-04T14:35:09Z","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":"5fc4901beb33998d944cef6828a9deac15e716f237f87e3e393cb27ac00e14d4","cross_cats_sorted":["math.GT"],"license":"","primary_cat":"math.DG","submitted_at":"2001-04-05T15:36:46Z","title_canon_sha256":"a227cce270865556870f0be0a228f2ae7d995c9357f6f52c32e027d4fd2bcade"},"schema_version":"1.0","source":{"id":"math/0104064","kind":"arxiv","version":1}},"canonical_sha256":"ab3acebde5c4bf392b81fafb1956f03a8d431943cf1c3b9e8f172d425334f83d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ab3acebde5c4bf392b81fafb1956f03a8d431943cf1c3b9e8f172d425334f83d","first_computed_at":"2026-07-04T14:35:09.350477Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:35:09.350477Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yXMhUjvs+ERR6FVLA1dWnEVSJRPWwV0nX/j0y/baC0S/rcBTU3wVoFfhSQ0PUHHHU75ky7KmrhsNjEqzV5yGBw==","signature_status":"signed_v1","signed_at":"2026-07-04T14:35:09.350804Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0104064","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4eb0ea3e15e49292d77625a3514c96e1898dab2dc6a402eb631ec245a4102cbd","sha256:711b7fcb515ab315c9344734fe76716188e6168c2a223be4e076b4f9eb323d57"],"state_sha256":"f49775c0bb2bffe340e1226c52aeab1388b1380e7158c44024d2855a59163e51"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xTnWxueEs7PqIKijbOoshQcqYvMrUVWQqhAyDAoSCO5qlYtlqde5ciPyJjtQbU2knk4TfIXQyL5TuH8P4PQWBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T11:43:39.762415Z","bundle_sha256":"76625617e5b3906e19aea72266930b5ac9b4303cb8b4e6922eb7adce080629d0"}}