{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:BT2AZ7GP4O6VWSRYQR2PL4QDCX","short_pith_number":"pith:BT2AZ7GP","canonical_record":{"source":{"id":"1803.00644","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-03-01T21:56:26Z","cross_cats_sorted":[],"title_canon_sha256":"09b9757fa6dfbaf5b0a1ed84811db6ddd032da2c3320c026350263c453f086fd","abstract_canon_sha256":"5b0b4f85edbcd9c0c6788422a3f7db614b6717302d2a44e77f006be762db776b"},"schema_version":"1.0"},"canonical_sha256":"0cf40cfccfe3bd5b4a388474f5f20315df6469ce107b4d5f882e6c3ade2b7b1e","source":{"kind":"arxiv","id":"1803.00644","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.00644","created_at":"2026-05-18T00:22:08Z"},{"alias_kind":"arxiv_version","alias_value":"1803.00644v1","created_at":"2026-05-18T00:22:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.00644","created_at":"2026-05-18T00:22:08Z"},{"alias_kind":"pith_short_12","alias_value":"BT2AZ7GP4O6V","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"BT2AZ7GP4O6VWSRY","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"BT2AZ7GP","created_at":"2026-05-18T12:32:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:BT2AZ7GP4O6VWSRYQR2PL4QDCX","target":"record","payload":{"canonical_record":{"source":{"id":"1803.00644","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-03-01T21:56:26Z","cross_cats_sorted":[],"title_canon_sha256":"09b9757fa6dfbaf5b0a1ed84811db6ddd032da2c3320c026350263c453f086fd","abstract_canon_sha256":"5b0b4f85edbcd9c0c6788422a3f7db614b6717302d2a44e77f006be762db776b"},"schema_version":"1.0"},"canonical_sha256":"0cf40cfccfe3bd5b4a388474f5f20315df6469ce107b4d5f882e6c3ade2b7b1e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:08.294075Z","signature_b64":"RGW070M9T2b0U5jC0EFxLLZ/N8v8nXqE0uEWGYR4sj1ZyqvEMEPhHyAVrFYsIcrOkSl8KDewhkvRHlbo/FmzCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0cf40cfccfe3bd5b4a388474f5f20315df6469ce107b4d5f882e6c3ade2b7b1e","last_reissued_at":"2026-05-18T00:22:08.293490Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:08.293490Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.00644","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":"2026-05-18T00:22:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LyHbvCC3wfxzya+8KqofOB4pJW9+4j1T+B9Dyr8REJPlPpvVuNEjJa9N6GNYEDdnS93wWNxmTxOMwIJtuVXnAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T11:00:36.807070Z"},"content_sha256":"aeeba953aec18cc6a80a77974987ec79b39640a7d6002a24c42550574dbaa62d","schema_version":"1.0","event_id":"sha256:aeeba953aec18cc6a80a77974987ec79b39640a7d6002a24c42550574dbaa62d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:BT2AZ7GP4O6VWSRYQR2PL4QDCX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized dunce hats are not splittable","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Fredric Ancel, Pete Sparks","submitted_at":"2018-03-01T21:56:26Z","abstract_excerpt":"A \\emph{generalized dunce hat} is a 2-dimensional polyhedron created by attaching the boundary of a disk $\\Delta$ to a circle $J$ via a map $f:\\partial \\Delta \\to J$ with the property that there is a point $v \\in J$ such that $f^{-1}(\\{v\\})$ is a finite set containing at least 3 points and $f$ maps each component of $\\partial \\Delta - f^{-1}(\\{v\\})$ homeomorphically onto $J - \\{v\\}.$ \\textbf{Theorem:} No generalized dunce hat is the union of two proper subpolyhedra that each have finite first homology groups. This result undermines a strategy for proving that the interior of the Mazur compact "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.00644","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":"2026-05-18T00:22:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y5YHCVaA6wRMeb8W6fvldJH4PG1CaHlNwZ1m7r2Ddbrt/qj1SciZuT34ZQ+Xb4nn5nNuSBpFWMsKrWWJxkmtBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T11:00:36.807444Z"},"content_sha256":"abed6a27d0a46024f2d0c131775fae8f3fe946fd418ee6c882c14c2abaa209f5","schema_version":"1.0","event_id":"sha256:abed6a27d0a46024f2d0c131775fae8f3fe946fd418ee6c882c14c2abaa209f5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BT2AZ7GP4O6VWSRYQR2PL4QDCX/bundle.json","state_url":"https://pith.science/pith/BT2AZ7GP4O6VWSRYQR2PL4QDCX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BT2AZ7GP4O6VWSRYQR2PL4QDCX/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":"2026-06-11T11:00:36Z","links":{"resolver":"https://pith.science/pith/BT2AZ7GP4O6VWSRYQR2PL4QDCX","bundle":"https://pith.science/pith/BT2AZ7GP4O6VWSRYQR2PL4QDCX/bundle.json","state":"https://pith.science/pith/BT2AZ7GP4O6VWSRYQR2PL4QDCX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BT2AZ7GP4O6VWSRYQR2PL4QDCX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:BT2AZ7GP4O6VWSRYQR2PL4QDCX","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":"5b0b4f85edbcd9c0c6788422a3f7db614b6717302d2a44e77f006be762db776b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-03-01T21:56:26Z","title_canon_sha256":"09b9757fa6dfbaf5b0a1ed84811db6ddd032da2c3320c026350263c453f086fd"},"schema_version":"1.0","source":{"id":"1803.00644","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.00644","created_at":"2026-05-18T00:22:08Z"},{"alias_kind":"arxiv_version","alias_value":"1803.00644v1","created_at":"2026-05-18T00:22:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.00644","created_at":"2026-05-18T00:22:08Z"},{"alias_kind":"pith_short_12","alias_value":"BT2AZ7GP4O6V","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"BT2AZ7GP4O6VWSRY","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"BT2AZ7GP","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:abed6a27d0a46024f2d0c131775fae8f3fe946fd418ee6c882c14c2abaa209f5","target":"graph","created_at":"2026-05-18T00:22:08Z","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":"A \\emph{generalized dunce hat} is a 2-dimensional polyhedron created by attaching the boundary of a disk $\\Delta$ to a circle $J$ via a map $f:\\partial \\Delta \\to J$ with the property that there is a point $v \\in J$ such that $f^{-1}(\\{v\\})$ is a finite set containing at least 3 points and $f$ maps each component of $\\partial \\Delta - f^{-1}(\\{v\\})$ homeomorphically onto $J - \\{v\\}.$ \\textbf{Theorem:} No generalized dunce hat is the union of two proper subpolyhedra that each have finite first homology groups. This result undermines a strategy for proving that the interior of the Mazur compact ","authors_text":"Fredric Ancel, Pete Sparks","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-03-01T21:56:26Z","title":"Generalized dunce hats are not splittable"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.00644","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:aeeba953aec18cc6a80a77974987ec79b39640a7d6002a24c42550574dbaa62d","target":"record","created_at":"2026-05-18T00:22:08Z","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":"5b0b4f85edbcd9c0c6788422a3f7db614b6717302d2a44e77f006be762db776b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-03-01T21:56:26Z","title_canon_sha256":"09b9757fa6dfbaf5b0a1ed84811db6ddd032da2c3320c026350263c453f086fd"},"schema_version":"1.0","source":{"id":"1803.00644","kind":"arxiv","version":1}},"canonical_sha256":"0cf40cfccfe3bd5b4a388474f5f20315df6469ce107b4d5f882e6c3ade2b7b1e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0cf40cfccfe3bd5b4a388474f5f20315df6469ce107b4d5f882e6c3ade2b7b1e","first_computed_at":"2026-05-18T00:22:08.293490Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:08.293490Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RGW070M9T2b0U5jC0EFxLLZ/N8v8nXqE0uEWGYR4sj1ZyqvEMEPhHyAVrFYsIcrOkSl8KDewhkvRHlbo/FmzCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:08.294075Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.00644","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aeeba953aec18cc6a80a77974987ec79b39640a7d6002a24c42550574dbaa62d","sha256:abed6a27d0a46024f2d0c131775fae8f3fe946fd418ee6c882c14c2abaa209f5"],"state_sha256":"38ab41ec883d6dfc29192385f3a316d3bbccc6b12538d41617dc075f5ccc82b1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5pxm/Kz8mDT9A5ve8pfyM1KVHXeJGNlip6lUlt/IJ7UmM/6WgR/nauJOVST35Ui9ToUo3MCH7X164Dr0N6dgCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T11:00:36.809454Z","bundle_sha256":"cf44b9ba963bd469e2da3886e1a8b916d08478c6faf317a09337d75b54412718"}}