{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:DVIUDLGG6TH7SVDYDACPPO6M2J","short_pith_number":"pith:DVIUDLGG","canonical_record":{"source":{"id":"0811.1678","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2008-11-11T10:43:04Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"9e5d321f49e50f9eee401722940a4adc06c92f426b48305c06199af2e4c6f4b2","abstract_canon_sha256":"e3fa45056259ebb6a55320bc9d8f6281c7e3d67044d5d8f1b1125a67c7be170c"},"schema_version":"1.0"},"canonical_sha256":"1d5141acc6f4cff954781804f7bbccd276a4108379837e0bb26b0a5f05fb9de0","source":{"kind":"arxiv","id":"0811.1678","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0811.1678","created_at":"2026-05-18T04:16:12Z"},{"alias_kind":"arxiv_version","alias_value":"0811.1678v1","created_at":"2026-05-18T04:16:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0811.1678","created_at":"2026-05-18T04:16:12Z"},{"alias_kind":"pith_short_12","alias_value":"DVIUDLGG6TH7","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"DVIUDLGG6TH7SVDY","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"DVIUDLGG","created_at":"2026-05-18T12:25:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:DVIUDLGG6TH7SVDYDACPPO6M2J","target":"record","payload":{"canonical_record":{"source":{"id":"0811.1678","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2008-11-11T10:43:04Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"9e5d321f49e50f9eee401722940a4adc06c92f426b48305c06199af2e4c6f4b2","abstract_canon_sha256":"e3fa45056259ebb6a55320bc9d8f6281c7e3d67044d5d8f1b1125a67c7be170c"},"schema_version":"1.0"},"canonical_sha256":"1d5141acc6f4cff954781804f7bbccd276a4108379837e0bb26b0a5f05fb9de0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:16:12.321551Z","signature_b64":"/amIbDQBVSNTDThIhAuddhI4TAV97BydUGYvO0ywYWqOq2joYp/mr7DRwtemnMAJeV1VMvsncdZGgxaVtrRVAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d5141acc6f4cff954781804f7bbccd276a4108379837e0bb26b0a5f05fb9de0","last_reissued_at":"2026-05-18T04:16:12.321037Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:16:12.321037Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0811.1678","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":"2026-05-18T04:16:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gyQNOIUgRNX9diB8UmUWrmnrnuz/zk+GJaNHkWG78m91aytbV0TGvvTOxzi6AOYvwcnXauS+Js7yqcprDk1JCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T12:03:56.041113Z"},"content_sha256":"adba6d11587f87414f710936b2c50f6b4cc9b8f4dc98023fc010ecd83f259abe","schema_version":"1.0","event_id":"sha256:adba6d11587f87414f710936b2c50f6b4cc9b8f4dc98023fc010ecd83f259abe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:DVIUDLGG6TH7SVDYDACPPO6M2J","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On hyperbolic once-punctured-torus bundles III: Comparing two tessellations of the complex plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Makoto Sakuma, Warren Dicks","submitted_at":"2008-11-11T10:43:04Z","abstract_excerpt":"To each once-punctured-torus bundle, $T_\\phi$, over the circle with pseudo-Anosov monodromy $\\phi$, there are associated two tessellations of the complex plane: one, $\\Delta(\\phi)$, is (the projection from $\\infty$ of) the triangulation of a horosphere at $\\infty$ induced by the canonical decomposition into ideal tetrahedra, and the other, $CW(\\phi)$, is a fractal tessellation given by the Cannon-Thurston map of the fiber group switching back and forth between gray and white each time it passes through $\\infty$. In this paper, we study the relation between $\\Delta(\\phi)$ and $CW(\\phi)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0811.1678","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":"2026-05-18T04:16:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YlQWgqoZwSzE9O0o8u2sBGql8zmRx9whD6ugEuKMvwnJ3yk0/nlu/hro5B+IDX39ZeQscbHQq7ACWk+2E3VYDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T12:03:56.041782Z"},"content_sha256":"1305ed0d7544a7917ad05787c62c823420271904219980bc293a71da8f42e70d","schema_version":"1.0","event_id":"sha256:1305ed0d7544a7917ad05787c62c823420271904219980bc293a71da8f42e70d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DVIUDLGG6TH7SVDYDACPPO6M2J/bundle.json","state_url":"https://pith.science/pith/DVIUDLGG6TH7SVDYDACPPO6M2J/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DVIUDLGG6TH7SVDYDACPPO6M2J/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":"2026-06-09T12:03:56Z","links":{"resolver":"https://pith.science/pith/DVIUDLGG6TH7SVDYDACPPO6M2J","bundle":"https://pith.science/pith/DVIUDLGG6TH7SVDYDACPPO6M2J/bundle.json","state":"https://pith.science/pith/DVIUDLGG6TH7SVDYDACPPO6M2J/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DVIUDLGG6TH7SVDYDACPPO6M2J/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:DVIUDLGG6TH7SVDYDACPPO6M2J","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":"e3fa45056259ebb6a55320bc9d8f6281c7e3d67044d5d8f1b1125a67c7be170c","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2008-11-11T10:43:04Z","title_canon_sha256":"9e5d321f49e50f9eee401722940a4adc06c92f426b48305c06199af2e4c6f4b2"},"schema_version":"1.0","source":{"id":"0811.1678","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0811.1678","created_at":"2026-05-18T04:16:12Z"},{"alias_kind":"arxiv_version","alias_value":"0811.1678v1","created_at":"2026-05-18T04:16:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0811.1678","created_at":"2026-05-18T04:16:12Z"},{"alias_kind":"pith_short_12","alias_value":"DVIUDLGG6TH7","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"DVIUDLGG6TH7SVDY","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"DVIUDLGG","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:1305ed0d7544a7917ad05787c62c823420271904219980bc293a71da8f42e70d","target":"graph","created_at":"2026-05-18T04:16:12Z","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":"To each once-punctured-torus bundle, $T_\\phi$, over the circle with pseudo-Anosov monodromy $\\phi$, there are associated two tessellations of the complex plane: one, $\\Delta(\\phi)$, is (the projection from $\\infty$ of) the triangulation of a horosphere at $\\infty$ induced by the canonical decomposition into ideal tetrahedra, and the other, $CW(\\phi)$, is a fractal tessellation given by the Cannon-Thurston map of the fiber group switching back and forth between gray and white each time it passes through $\\infty$. In this paper, we study the relation between $\\Delta(\\phi)$ and $CW(\\phi)$.","authors_text":"Makoto Sakuma, Warren Dicks","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2008-11-11T10:43:04Z","title":"On hyperbolic once-punctured-torus bundles III: Comparing two tessellations of the complex plane"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0811.1678","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:adba6d11587f87414f710936b2c50f6b4cc9b8f4dc98023fc010ecd83f259abe","target":"record","created_at":"2026-05-18T04:16:12Z","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":"e3fa45056259ebb6a55320bc9d8f6281c7e3d67044d5d8f1b1125a67c7be170c","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2008-11-11T10:43:04Z","title_canon_sha256":"9e5d321f49e50f9eee401722940a4adc06c92f426b48305c06199af2e4c6f4b2"},"schema_version":"1.0","source":{"id":"0811.1678","kind":"arxiv","version":1}},"canonical_sha256":"1d5141acc6f4cff954781804f7bbccd276a4108379837e0bb26b0a5f05fb9de0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1d5141acc6f4cff954781804f7bbccd276a4108379837e0bb26b0a5f05fb9de0","first_computed_at":"2026-05-18T04:16:12.321037Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:16:12.321037Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/amIbDQBVSNTDThIhAuddhI4TAV97BydUGYvO0ywYWqOq2joYp/mr7DRwtemnMAJeV1VMvsncdZGgxaVtrRVAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:16:12.321551Z","signed_message":"canonical_sha256_bytes"},"source_id":"0811.1678","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:adba6d11587f87414f710936b2c50f6b4cc9b8f4dc98023fc010ecd83f259abe","sha256:1305ed0d7544a7917ad05787c62c823420271904219980bc293a71da8f42e70d"],"state_sha256":"bb811c77960a20df5cc8f88455cb1ad2369a642126b491c1eee6969f83803d86"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2FCu5VyK1GED9HHgkNwfKON1CQnL4e9W/ejsp5cfwJMHiS4NGrfzGd9rIHIdES2zBzEHlodbL1wMlUyFcpIaBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T12:03:56.046459Z","bundle_sha256":"766b9561a395e19db7a095a92763fee5fce972ad2324bb83d70643247bc4d394"}}