{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:IBZVZCGZVQJMA4YZELFZ7U3VAP","short_pith_number":"pith:IBZVZCGZ","canonical_record":{"source":{"id":"1512.08341","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-12-28T08:39:06Z","cross_cats_sorted":[],"title_canon_sha256":"5bfbbd283abbfc87deb28e6e45135846cef4d48ff6df2688e97a5fd5b272ca4d","abstract_canon_sha256":"8e5372444d3e6ded4c05a16eb2f3307e3c567dfb39a5efbfe653519dbac2c322"},"schema_version":"1.0"},"canonical_sha256":"40735c88d9ac12c0731922cb9fd37503f8b3d1d0d4870ca8e58b56d2b058b382","source":{"kind":"arxiv","id":"1512.08341","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.08341","created_at":"2026-05-18T01:23:15Z"},{"alias_kind":"arxiv_version","alias_value":"1512.08341v2","created_at":"2026-05-18T01:23:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.08341","created_at":"2026-05-18T01:23:15Z"},{"alias_kind":"pith_short_12","alias_value":"IBZVZCGZVQJM","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"IBZVZCGZVQJMA4YZ","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"IBZVZCGZ","created_at":"2026-05-18T12:29:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:IBZVZCGZVQJMA4YZELFZ7U3VAP","target":"record","payload":{"canonical_record":{"source":{"id":"1512.08341","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-12-28T08:39:06Z","cross_cats_sorted":[],"title_canon_sha256":"5bfbbd283abbfc87deb28e6e45135846cef4d48ff6df2688e97a5fd5b272ca4d","abstract_canon_sha256":"8e5372444d3e6ded4c05a16eb2f3307e3c567dfb39a5efbfe653519dbac2c322"},"schema_version":"1.0"},"canonical_sha256":"40735c88d9ac12c0731922cb9fd37503f8b3d1d0d4870ca8e58b56d2b058b382","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:15.845044Z","signature_b64":"9p2jV4WrVcpUd0/A0GdCmbGtDS8ivPgRJbtTovrOnu1JQx2kdj40eamDoz522TugBLwXazn6jM3GOt4j0QITDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"40735c88d9ac12c0731922cb9fd37503f8b3d1d0d4870ca8e58b56d2b058b382","last_reissued_at":"2026-05-18T01:23:15.844497Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:15.844497Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.08341","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":"2026-05-18T01:23:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ABPGwvcatixjzk3O/AXGW3cmTK5w02jTrQ4Uy+FTybMg7/Vj3Ojn8g+2mEVFGfsr9AMlPzDKaK6HA36FZwlVAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T22:31:30.303708Z"},"content_sha256":"80f2700c7e86b0f74ff5526e247f9630684ddbd4842b397f1e595cbf4a6f11a5","schema_version":"1.0","event_id":"sha256:80f2700c7e86b0f74ff5526e247f9630684ddbd4842b397f1e595cbf4a6f11a5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:IBZVZCGZVQJMA4YZELFZ7U3VAP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Counting components of an integral lamination","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"S. Oyku Yurttas, Toby Hall","submitted_at":"2015-12-28T08:39:06Z","abstract_excerpt":"We present an efficient algorithm for calculating the number of components of an integral lamination on an $n$-punctured disk, given its Dynnikov coordinates. The algorithm requires $O(n^2M)$ arithmetic operations, where $M$ is the sum of the absolute values of the Dynnikov coordinates."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08341","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":"2026-05-18T01:23:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DIAjoSPQUHB4TDXrQ5jdS9g0xmXI/rAwnVCJcgr6C94l6wdwtVLn/LiL5mKweaxvdySuYtamiCUSfvVSBtxgBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T22:31:30.304419Z"},"content_sha256":"fba7d2e9023aec0723afb6524195dbf6b2cee0576bbacab8128fe10e8f8235a4","schema_version":"1.0","event_id":"sha256:fba7d2e9023aec0723afb6524195dbf6b2cee0576bbacab8128fe10e8f8235a4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IBZVZCGZVQJMA4YZELFZ7U3VAP/bundle.json","state_url":"https://pith.science/pith/IBZVZCGZVQJMA4YZELFZ7U3VAP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IBZVZCGZVQJMA4YZELFZ7U3VAP/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":"2026-06-06T22:31:30Z","links":{"resolver":"https://pith.science/pith/IBZVZCGZVQJMA4YZELFZ7U3VAP","bundle":"https://pith.science/pith/IBZVZCGZVQJMA4YZELFZ7U3VAP/bundle.json","state":"https://pith.science/pith/IBZVZCGZVQJMA4YZELFZ7U3VAP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IBZVZCGZVQJMA4YZELFZ7U3VAP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:IBZVZCGZVQJMA4YZELFZ7U3VAP","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":"8e5372444d3e6ded4c05a16eb2f3307e3c567dfb39a5efbfe653519dbac2c322","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-12-28T08:39:06Z","title_canon_sha256":"5bfbbd283abbfc87deb28e6e45135846cef4d48ff6df2688e97a5fd5b272ca4d"},"schema_version":"1.0","source":{"id":"1512.08341","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.08341","created_at":"2026-05-18T01:23:15Z"},{"alias_kind":"arxiv_version","alias_value":"1512.08341v2","created_at":"2026-05-18T01:23:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.08341","created_at":"2026-05-18T01:23:15Z"},{"alias_kind":"pith_short_12","alias_value":"IBZVZCGZVQJM","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"IBZVZCGZVQJMA4YZ","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"IBZVZCGZ","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:fba7d2e9023aec0723afb6524195dbf6b2cee0576bbacab8128fe10e8f8235a4","target":"graph","created_at":"2026-05-18T01:23:15Z","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 present an efficient algorithm for calculating the number of components of an integral lamination on an $n$-punctured disk, given its Dynnikov coordinates. The algorithm requires $O(n^2M)$ arithmetic operations, where $M$ is the sum of the absolute values of the Dynnikov coordinates.","authors_text":"S. Oyku Yurttas, Toby Hall","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-12-28T08:39:06Z","title":"Counting components of an integral lamination"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08341","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":"sha256:80f2700c7e86b0f74ff5526e247f9630684ddbd4842b397f1e595cbf4a6f11a5","target":"record","created_at":"2026-05-18T01:23:15Z","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":"8e5372444d3e6ded4c05a16eb2f3307e3c567dfb39a5efbfe653519dbac2c322","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-12-28T08:39:06Z","title_canon_sha256":"5bfbbd283abbfc87deb28e6e45135846cef4d48ff6df2688e97a5fd5b272ca4d"},"schema_version":"1.0","source":{"id":"1512.08341","kind":"arxiv","version":2}},"canonical_sha256":"40735c88d9ac12c0731922cb9fd37503f8b3d1d0d4870ca8e58b56d2b058b382","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"40735c88d9ac12c0731922cb9fd37503f8b3d1d0d4870ca8e58b56d2b058b382","first_computed_at":"2026-05-18T01:23:15.844497Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:15.844497Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9p2jV4WrVcpUd0/A0GdCmbGtDS8ivPgRJbtTovrOnu1JQx2kdj40eamDoz522TugBLwXazn6jM3GOt4j0QITDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:15.845044Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.08341","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:80f2700c7e86b0f74ff5526e247f9630684ddbd4842b397f1e595cbf4a6f11a5","sha256:fba7d2e9023aec0723afb6524195dbf6b2cee0576bbacab8128fe10e8f8235a4"],"state_sha256":"86df6c6aeb5ce40e499995b6904dae7c10f2c5009c111617c73d66952d31ed3d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o2ZbrfyL6vpOMNhFlVih7zOfMoFJ7eGl9bK5gKShCV0zLLOeLfpKUPcp73VHeJEwtW3VCtG/MfJoQgIV2RZYAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T22:31:30.311146Z","bundle_sha256":"06823b6394f8b682da47bcd97fe8c509e2fbef96582c87943e8753c1adfe7e89"}}