{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:T3HPDUV3I2RBTNABNR7CEYORPG","short_pith_number":"pith:T3HPDUV3","canonical_record":{"source":{"id":"2110.10716","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2021-10-20T18:26:10Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"e6fbc19862c8c46369d331262bc8ffa864286cea335df9ce4d7e11896c680165","abstract_canon_sha256":"fb03fd544936d8e939e906f2c395d7fb7f67b4331b5e2d18ad0c78ac4a3e22fe"},"schema_version":"1.0"},"canonical_sha256":"9ecef1d2bb46a219b4016c7e2261d179b0ccffcb28ce7ead6c91ea6f4e186320","source":{"kind":"arxiv","id":"2110.10716","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.10716","created_at":"2026-07-05T03:24:20Z"},{"alias_kind":"arxiv_version","alias_value":"2110.10716v1","created_at":"2026-07-05T03:24:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.10716","created_at":"2026-07-05T03:24:20Z"},{"alias_kind":"pith_short_12","alias_value":"T3HPDUV3I2RB","created_at":"2026-07-05T03:24:20Z"},{"alias_kind":"pith_short_16","alias_value":"T3HPDUV3I2RBTNAB","created_at":"2026-07-05T03:24:20Z"},{"alias_kind":"pith_short_8","alias_value":"T3HPDUV3","created_at":"2026-07-05T03:24:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:T3HPDUV3I2RBTNABNR7CEYORPG","target":"record","payload":{"canonical_record":{"source":{"id":"2110.10716","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2021-10-20T18:26:10Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"e6fbc19862c8c46369d331262bc8ffa864286cea335df9ce4d7e11896c680165","abstract_canon_sha256":"fb03fd544936d8e939e906f2c395d7fb7f67b4331b5e2d18ad0c78ac4a3e22fe"},"schema_version":"1.0"},"canonical_sha256":"9ecef1d2bb46a219b4016c7e2261d179b0ccffcb28ce7ead6c91ea6f4e186320","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:24:20.482674Z","signature_b64":"gKCwFsPEbmpOIshvtiNRRP4wCat/eZnv6J5DGwLikItR3FzfQNMabk/q1x/AvZX+sKcSkaV9vXnOwS6jMEYZCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9ecef1d2bb46a219b4016c7e2261d179b0ccffcb28ce7ead6c91ea6f4e186320","last_reissued_at":"2026-07-05T03:24:20.482231Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:24:20.482231Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2110.10716","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":"2026-07-05T03:24:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PB9jZ35A2kkIFJS6SkRWVqwmkfXzAvev1SKfRCpYqH90iuyZRacrlUYzZdB4910KN1151gfJqS2Jo6st6IjGAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T04:26:36.728315Z"},"content_sha256":"29af914c078d08ff80a340531b4d40828b465f86a2e4c0cf813466b94618be7e","schema_version":"1.0","event_id":"sha256:29af914c078d08ff80a340531b4d40828b465f86a2e4c0cf813466b94618be7e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:T3HPDUV3I2RBTNABNR7CEYORPG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Floer homology, twist coefficients, and capping off","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.GT","authors_text":"Braeden Reinoso","submitted_at":"2021-10-20T18:26:10Z","abstract_excerpt":"For an open book decomposition $(S,\\phi)$, the fractional Dehn twist coefficients are rational numbers measuring the amount that the monodromy $\\phi$ twists the surface $S$ near each boundary component. In general, the twist coefficients do not behave nicely under the operation of capping off a boundary component. The goal of this paper is to use Heegaard Floer homology to constrain the behavior of the fractional Dehn twist coefficients after capping off. We also use our results about fractional Dehn twists to study the Floer homology of cyclic branched covers over fibered two-component links."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.10716","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/2110.10716/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":"2026-07-05T03:24:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3JOgRZPQVXIZwnqwW0hvVnrkfB+Jjgk8zCxy/Y8gUVH2mkSGA+u6kBa8CEX39Sd0MLJkYfyxtw5VlascXEGOCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T04:26:36.729825Z"},"content_sha256":"dedd3698acc5f89b4b93823734fa8b74a5b9e81ff6f7a0fe6ac283ecacf5c180","schema_version":"1.0","event_id":"sha256:dedd3698acc5f89b4b93823734fa8b74a5b9e81ff6f7a0fe6ac283ecacf5c180"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T3HPDUV3I2RBTNABNR7CEYORPG/bundle.json","state_url":"https://pith.science/pith/T3HPDUV3I2RBTNABNR7CEYORPG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T3HPDUV3I2RBTNABNR7CEYORPG/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":"2026-08-20T04:26:36Z","links":{"resolver":"https://pith.science/pith/T3HPDUV3I2RBTNABNR7CEYORPG","bundle":"https://pith.science/pith/T3HPDUV3I2RBTNABNR7CEYORPG/bundle.json","state":"https://pith.science/pith/T3HPDUV3I2RBTNABNR7CEYORPG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T3HPDUV3I2RBTNABNR7CEYORPG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:T3HPDUV3I2RBTNABNR7CEYORPG","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":"fb03fd544936d8e939e906f2c395d7fb7f67b4331b5e2d18ad0c78ac4a3e22fe","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2021-10-20T18:26:10Z","title_canon_sha256":"e6fbc19862c8c46369d331262bc8ffa864286cea335df9ce4d7e11896c680165"},"schema_version":"1.0","source":{"id":"2110.10716","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.10716","created_at":"2026-07-05T03:24:20Z"},{"alias_kind":"arxiv_version","alias_value":"2110.10716v1","created_at":"2026-07-05T03:24:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.10716","created_at":"2026-07-05T03:24:20Z"},{"alias_kind":"pith_short_12","alias_value":"T3HPDUV3I2RB","created_at":"2026-07-05T03:24:20Z"},{"alias_kind":"pith_short_16","alias_value":"T3HPDUV3I2RBTNAB","created_at":"2026-07-05T03:24:20Z"},{"alias_kind":"pith_short_8","alias_value":"T3HPDUV3","created_at":"2026-07-05T03:24:20Z"}],"graph_snapshots":[{"event_id":"sha256:dedd3698acc5f89b4b93823734fa8b74a5b9e81ff6f7a0fe6ac283ecacf5c180","target":"graph","created_at":"2026-07-05T03:24:20Z","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/2110.10716/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For an open book decomposition $(S,\\phi)$, the fractional Dehn twist coefficients are rational numbers measuring the amount that the monodromy $\\phi$ twists the surface $S$ near each boundary component. In general, the twist coefficients do not behave nicely under the operation of capping off a boundary component. The goal of this paper is to use Heegaard Floer homology to constrain the behavior of the fractional Dehn twist coefficients after capping off. We also use our results about fractional Dehn twists to study the Floer homology of cyclic branched covers over fibered two-component links.","authors_text":"Braeden Reinoso","cross_cats":["math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2021-10-20T18:26:10Z","title":"Floer homology, twist coefficients, and capping off"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.10716","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":"sha256:29af914c078d08ff80a340531b4d40828b465f86a2e4c0cf813466b94618be7e","target":"record","created_at":"2026-07-05T03:24:20Z","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":"fb03fd544936d8e939e906f2c395d7fb7f67b4331b5e2d18ad0c78ac4a3e22fe","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2021-10-20T18:26:10Z","title_canon_sha256":"e6fbc19862c8c46369d331262bc8ffa864286cea335df9ce4d7e11896c680165"},"schema_version":"1.0","source":{"id":"2110.10716","kind":"arxiv","version":1}},"canonical_sha256":"9ecef1d2bb46a219b4016c7e2261d179b0ccffcb28ce7ead6c91ea6f4e186320","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9ecef1d2bb46a219b4016c7e2261d179b0ccffcb28ce7ead6c91ea6f4e186320","first_computed_at":"2026-07-05T03:24:20.482231Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:24:20.482231Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gKCwFsPEbmpOIshvtiNRRP4wCat/eZnv6J5DGwLikItR3FzfQNMabk/q1x/AvZX+sKcSkaV9vXnOwS6jMEYZCg==","signature_status":"signed_v1","signed_at":"2026-07-05T03:24:20.482674Z","signed_message":"canonical_sha256_bytes"},"source_id":"2110.10716","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:29af914c078d08ff80a340531b4d40828b465f86a2e4c0cf813466b94618be7e","sha256:dedd3698acc5f89b4b93823734fa8b74a5b9e81ff6f7a0fe6ac283ecacf5c180"],"state_sha256":"9410950fd85d558bcdebbb608084d431689a7b49374322e503fa2760ae668a37"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/3usDVe+VwnstvVVYdFq6+otLrYbkyERV3e8+6zE6v9WRkpgtWL77prjXl8rQjYSC+F93zLAzGC+7xfxPQ5HBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-20T04:26:36.738291Z","bundle_sha256":"cc1a3955ba7b3ae7d149a844fbf3d6fd5504f339cee623100391c0c7806d25d2"}}