{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:O7LVQMBISCCIUIDTBLZSWIPN5R","short_pith_number":"pith:O7LVQMBI","canonical_record":{"source":{"id":"1511.02851","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2015-11-08T02:07:12Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"cf4af1c380e0761d82c07532dcc265587664ffa9832fef568d84ae5dc22239f7","abstract_canon_sha256":"ec2e32b714f776bc00afa8b4d88c76a65ac3328e567babda68ba30816bf4d202"},"schema_version":"1.0"},"canonical_sha256":"77d758302890848a20730af32b21edec471d12914bb3e5a1d1bd1f08e37e0a71","source":{"kind":"arxiv","id":"1511.02851","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.02851","created_at":"2026-05-18T00:58:55Z"},{"alias_kind":"arxiv_version","alias_value":"1511.02851v2","created_at":"2026-05-18T00:58:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.02851","created_at":"2026-05-18T00:58:55Z"},{"alias_kind":"pith_short_12","alias_value":"O7LVQMBISCCI","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"O7LVQMBISCCIUIDT","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"O7LVQMBI","created_at":"2026-05-18T12:29:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:O7LVQMBISCCIUIDTBLZSWIPN5R","target":"record","payload":{"canonical_record":{"source":{"id":"1511.02851","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2015-11-08T02:07:12Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"cf4af1c380e0761d82c07532dcc265587664ffa9832fef568d84ae5dc22239f7","abstract_canon_sha256":"ec2e32b714f776bc00afa8b4d88c76a65ac3328e567babda68ba30816bf4d202"},"schema_version":"1.0"},"canonical_sha256":"77d758302890848a20730af32b21edec471d12914bb3e5a1d1bd1f08e37e0a71","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:58:55.442422Z","signature_b64":"PPElWuDDBudgBeZJ9rT2txnGS71mv8oF8K7Q41Ibej2fQVY8xGTBdK5mi1Hkp5F6R42Mg5zz8ZaA0hcU3RSgCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"77d758302890848a20730af32b21edec471d12914bb3e5a1d1bd1f08e37e0a71","last_reissued_at":"2026-05-18T00:58:55.441889Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:58:55.441889Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.02851","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":"2026-05-18T00:58:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"icbq5tAs9FIYjZJr0bSwlIK2XV1YNvYnUh9u33i2wzpaI0XH1L0513KsOOunaGNgLUK+bQsH4cYioM50cm+OBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T19:50:23.515708Z"},"content_sha256":"09ed094861ef230562b8c9025337b66bec6533663a350c31d03e8927f949980a","schema_version":"1.0","event_id":"sha256:09ed094861ef230562b8c9025337b66bec6533663a350c31d03e8927f949980a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:O7LVQMBISCCIUIDTBLZSWIPN5R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Visualizing Hyperbolic Honeycombs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.HO","authors_text":"Henry Segerman, Roice Nelson","submitted_at":"2015-11-08T02:07:12Z","abstract_excerpt":"We explore visual representations of tilings corresponding to Schl\\\"afli symbols. In three dimensions, we call these tilings \"honeycombs\". Schl\\\"afli symbols encode, in a very efficient way, regular tilings of spherical, euclidean and hyperbolic spaces in all dimensions. In three dimensions, there are only a finite number of spherical and euclidean honeycombs, but infinitely many hyperbolic honeycombs. Moreover, there are only four hyperbolic honeycombs with material vertices and material cells (the cells are entirely inside of hyperbolic space), eleven with ideal vertices or cells (the cells "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.02851","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":"2026-05-18T00:58:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fxO4HI9DOd3qfuJ06LC4g+sf19Qe84+32JI71arXvejXioThBUDUw8LwSX/wXJGttmOY1N7YBvmDr9AOy8yiCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T19:50:23.516067Z"},"content_sha256":"16c3c942eabeb25c55d07a97c4b70d5a3c51d51b64b2128310b42e1dd26e6381","schema_version":"1.0","event_id":"sha256:16c3c942eabeb25c55d07a97c4b70d5a3c51d51b64b2128310b42e1dd26e6381"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O7LVQMBISCCIUIDTBLZSWIPN5R/bundle.json","state_url":"https://pith.science/pith/O7LVQMBISCCIUIDTBLZSWIPN5R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O7LVQMBISCCIUIDTBLZSWIPN5R/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":"2026-06-10T19:50:23Z","links":{"resolver":"https://pith.science/pith/O7LVQMBISCCIUIDTBLZSWIPN5R","bundle":"https://pith.science/pith/O7LVQMBISCCIUIDTBLZSWIPN5R/bundle.json","state":"https://pith.science/pith/O7LVQMBISCCIUIDTBLZSWIPN5R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O7LVQMBISCCIUIDTBLZSWIPN5R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:O7LVQMBISCCIUIDTBLZSWIPN5R","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":"ec2e32b714f776bc00afa8b4d88c76a65ac3328e567babda68ba30816bf4d202","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2015-11-08T02:07:12Z","title_canon_sha256":"cf4af1c380e0761d82c07532dcc265587664ffa9832fef568d84ae5dc22239f7"},"schema_version":"1.0","source":{"id":"1511.02851","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.02851","created_at":"2026-05-18T00:58:55Z"},{"alias_kind":"arxiv_version","alias_value":"1511.02851v2","created_at":"2026-05-18T00:58:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.02851","created_at":"2026-05-18T00:58:55Z"},{"alias_kind":"pith_short_12","alias_value":"O7LVQMBISCCI","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"O7LVQMBISCCIUIDT","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"O7LVQMBI","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:16c3c942eabeb25c55d07a97c4b70d5a3c51d51b64b2128310b42e1dd26e6381","target":"graph","created_at":"2026-05-18T00:58:55Z","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 explore visual representations of tilings corresponding to Schl\\\"afli symbols. In three dimensions, we call these tilings \"honeycombs\". Schl\\\"afli symbols encode, in a very efficient way, regular tilings of spherical, euclidean and hyperbolic spaces in all dimensions. In three dimensions, there are only a finite number of spherical and euclidean honeycombs, but infinitely many hyperbolic honeycombs. Moreover, there are only four hyperbolic honeycombs with material vertices and material cells (the cells are entirely inside of hyperbolic space), eleven with ideal vertices or cells (the cells ","authors_text":"Henry Segerman, Roice Nelson","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2015-11-08T02:07:12Z","title":"Visualizing Hyperbolic Honeycombs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.02851","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":"sha256:09ed094861ef230562b8c9025337b66bec6533663a350c31d03e8927f949980a","target":"record","created_at":"2026-05-18T00:58:55Z","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":"ec2e32b714f776bc00afa8b4d88c76a65ac3328e567babda68ba30816bf4d202","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2015-11-08T02:07:12Z","title_canon_sha256":"cf4af1c380e0761d82c07532dcc265587664ffa9832fef568d84ae5dc22239f7"},"schema_version":"1.0","source":{"id":"1511.02851","kind":"arxiv","version":2}},"canonical_sha256":"77d758302890848a20730af32b21edec471d12914bb3e5a1d1bd1f08e37e0a71","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"77d758302890848a20730af32b21edec471d12914bb3e5a1d1bd1f08e37e0a71","first_computed_at":"2026-05-18T00:58:55.441889Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:58:55.441889Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PPElWuDDBudgBeZJ9rT2txnGS71mv8oF8K7Q41Ibej2fQVY8xGTBdK5mi1Hkp5F6R42Mg5zz8ZaA0hcU3RSgCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:58:55.442422Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.02851","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:09ed094861ef230562b8c9025337b66bec6533663a350c31d03e8927f949980a","sha256:16c3c942eabeb25c55d07a97c4b70d5a3c51d51b64b2128310b42e1dd26e6381"],"state_sha256":"60a91f9f2d808d6f7d49fb50f611cfc6bccbaf5756cb1b7de0682078d6cbd6c0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vcx/8pKEikYnmpe9X3UZ4CIkl8kGEMPN3DEXEDthilZuc1i3OmQUPTowWJQ8Zpv6WRdZ9XlmfwReBE8meRbUBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T19:50:23.518002Z","bundle_sha256":"751bc9989779d84b0847c96537b87a560603376aa943d22c3ba3cedda3cbef60"}}