{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:KNKR33GIA3VCA7C6XVVTWCT7E7","short_pith_number":"pith:KNKR33GI","canonical_record":{"source":{"id":"2511.07796","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-11-11T03:28:49Z","cross_cats_sorted":[],"title_canon_sha256":"ac6ced81406d19ad24b63292ca98210934e308e8fb690b55ee0be38a36bece40","abstract_canon_sha256":"461c654bc2abbf60d2cd05e09fa3e9f5dc68e1a7920c98978f7dd3d1825a8410"},"schema_version":"1.0"},"canonical_sha256":"53551decc806ea207c5ebd6b3b0a7f27d8df45c71281f008a8b71bc440de1b62","source":{"kind":"arxiv","id":"2511.07796","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2511.07796","created_at":"2026-07-16T01:22:30Z"},{"alias_kind":"arxiv_version","alias_value":"2511.07796v3","created_at":"2026-07-16T01:22:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2511.07796","created_at":"2026-07-16T01:22:30Z"},{"alias_kind":"pith_short_12","alias_value":"KNKR33GIA3VC","created_at":"2026-07-16T01:22:30Z"},{"alias_kind":"pith_short_16","alias_value":"KNKR33GIA3VCA7C6","created_at":"2026-07-16T01:22:30Z"},{"alias_kind":"pith_short_8","alias_value":"KNKR33GI","created_at":"2026-07-16T01:22:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:KNKR33GIA3VCA7C6XVVTWCT7E7","target":"record","payload":{"canonical_record":{"source":{"id":"2511.07796","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-11-11T03:28:49Z","cross_cats_sorted":[],"title_canon_sha256":"ac6ced81406d19ad24b63292ca98210934e308e8fb690b55ee0be38a36bece40","abstract_canon_sha256":"461c654bc2abbf60d2cd05e09fa3e9f5dc68e1a7920c98978f7dd3d1825a8410"},"schema_version":"1.0"},"canonical_sha256":"53551decc806ea207c5ebd6b3b0a7f27d8df45c71281f008a8b71bc440de1b62","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-16T01:22:30.077213Z","signature_b64":"BmCmaRtTRUMb/1UyZshmZeeTvoGbLzBMutf5XdoFl+s51+dGQZqkfPISGY0w8ZZzMav31TeXH0wErH45EIq+AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"53551decc806ea207c5ebd6b3b0a7f27d8df45c71281f008a8b71bc440de1b62","last_reissued_at":"2026-07-16T01:22:30.076191Z","signature_status":"signed_v1","first_computed_at":"2026-07-16T01:22:30.076191Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2511.07796","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-16T01:22:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Dk3jjjvgO2fkl+/dEO2+UkbXSLBvUL84dKLbFISIdqMPbEPwrUSGrf/89jWUiVu8GdjPaMllFAurTw5NG+ZKBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T02:42:10.834981Z"},"content_sha256":"acdf567b865f08b21b65f65a801cd6f9a5f060acc659758bfad8ff118dec2819","schema_version":"1.0","event_id":"sha256:acdf567b865f08b21b65f65a801cd6f9a5f060acc659758bfad8ff118dec2819"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:KNKR33GIA3VCA7C6XVVTWCT7E7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Handlebody-knots obtained by tangle replacement","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Giovanni Bellettini, Giovanni Paolini, Maurizio Paolini, Yi-Sheng Wang","submitted_at":"2025-11-11T03:28:49Z","abstract_excerpt":"We study tangle replacement in the context of handlebody-knots. The main results classify the handlebody-knots obtained by performing tangle replacement on the prime spatial handcuff graph with four crossings, and determine their symmetry. The work is motivated by the study of small crossing handlebody-knots that are difficult to distinguish with computational invariants and by their chirality problem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2511.07796","kind":"arxiv","version":3},"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/2511.07796/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":"2026-07-16T01:22:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bsIsXyfGPLRBYtWUskOg+KdPyVsuKlG26II9BF42qL1bntlvEZMrFhU0uqWoYnR069yUjn+tp6KVB3NZv5YKCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T02:42:10.835755Z"},"content_sha256":"d83cf5961913d770ea7c2b18e10d0db72404b92467701027f585196f1c78dd8d","schema_version":"1.0","event_id":"sha256:d83cf5961913d770ea7c2b18e10d0db72404b92467701027f585196f1c78dd8d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KNKR33GIA3VCA7C6XVVTWCT7E7/bundle.json","state_url":"https://pith.science/pith/KNKR33GIA3VCA7C6XVVTWCT7E7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KNKR33GIA3VCA7C6XVVTWCT7E7/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":"2026-08-17T02:42:10Z","links":{"resolver":"https://pith.science/pith/KNKR33GIA3VCA7C6XVVTWCT7E7","bundle":"https://pith.science/pith/KNKR33GIA3VCA7C6XVVTWCT7E7/bundle.json","state":"https://pith.science/pith/KNKR33GIA3VCA7C6XVVTWCT7E7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KNKR33GIA3VCA7C6XVVTWCT7E7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:KNKR33GIA3VCA7C6XVVTWCT7E7","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":"461c654bc2abbf60d2cd05e09fa3e9f5dc68e1a7920c98978f7dd3d1825a8410","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-11-11T03:28:49Z","title_canon_sha256":"ac6ced81406d19ad24b63292ca98210934e308e8fb690b55ee0be38a36bece40"},"schema_version":"1.0","source":{"id":"2511.07796","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2511.07796","created_at":"2026-07-16T01:22:30Z"},{"alias_kind":"arxiv_version","alias_value":"2511.07796v3","created_at":"2026-07-16T01:22:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2511.07796","created_at":"2026-07-16T01:22:30Z"},{"alias_kind":"pith_short_12","alias_value":"KNKR33GIA3VC","created_at":"2026-07-16T01:22:30Z"},{"alias_kind":"pith_short_16","alias_value":"KNKR33GIA3VCA7C6","created_at":"2026-07-16T01:22:30Z"},{"alias_kind":"pith_short_8","alias_value":"KNKR33GI","created_at":"2026-07-16T01:22:30Z"}],"graph_snapshots":[{"event_id":"sha256:d83cf5961913d770ea7c2b18e10d0db72404b92467701027f585196f1c78dd8d","target":"graph","created_at":"2026-07-16T01:22:30Z","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/2511.07796/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study tangle replacement in the context of handlebody-knots. The main results classify the handlebody-knots obtained by performing tangle replacement on the prime spatial handcuff graph with four crossings, and determine their symmetry. The work is motivated by the study of small crossing handlebody-knots that are difficult to distinguish with computational invariants and by their chirality problem.","authors_text":"Giovanni Bellettini, Giovanni Paolini, Maurizio Paolini, Yi-Sheng Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-11-11T03:28:49Z","title":"Handlebody-knots obtained by tangle replacement"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2511.07796","kind":"arxiv","version":3},"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:acdf567b865f08b21b65f65a801cd6f9a5f060acc659758bfad8ff118dec2819","target":"record","created_at":"2026-07-16T01:22:30Z","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":"461c654bc2abbf60d2cd05e09fa3e9f5dc68e1a7920c98978f7dd3d1825a8410","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-11-11T03:28:49Z","title_canon_sha256":"ac6ced81406d19ad24b63292ca98210934e308e8fb690b55ee0be38a36bece40"},"schema_version":"1.0","source":{"id":"2511.07796","kind":"arxiv","version":3}},"canonical_sha256":"53551decc806ea207c5ebd6b3b0a7f27d8df45c71281f008a8b71bc440de1b62","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"53551decc806ea207c5ebd6b3b0a7f27d8df45c71281f008a8b71bc440de1b62","first_computed_at":"2026-07-16T01:22:30.076191Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-16T01:22:30.076191Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BmCmaRtTRUMb/1UyZshmZeeTvoGbLzBMutf5XdoFl+s51+dGQZqkfPISGY0w8ZZzMav31TeXH0wErH45EIq+AA==","signature_status":"signed_v1","signed_at":"2026-07-16T01:22:30.077213Z","signed_message":"canonical_sha256_bytes"},"source_id":"2511.07796","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:acdf567b865f08b21b65f65a801cd6f9a5f060acc659758bfad8ff118dec2819","sha256:d83cf5961913d770ea7c2b18e10d0db72404b92467701027f585196f1c78dd8d"],"state_sha256":"3899ba36ce400759247e4bb886c9182845a896cf206e9c442471215e33fea566"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S2VXaeG2GtyrG9o4LUwuXDeuOMHnJTj3vi+Ng3FdyOCVyAZ1NXd/3qoErUPyoPSYmKDZpjv/c38Q68PJGDsyBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T02:42:10.842515Z","bundle_sha256":"a6266aa8de00d59dc0739a88e16beda8685d487cf404d5c5cd719c870873c4a5"}}