{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:K6FHJLDMVTHYJ6MRF4EYGCP5BR","short_pith_number":"pith:K6FHJLDM","canonical_record":{"source":{"id":"1209.6532","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-09-28T14:23:57Z","cross_cats_sorted":[],"title_canon_sha256":"fc85b96f1a0b3face4df68c285db90b3d40df17e64bf27a641ae8ff2411352d6","abstract_canon_sha256":"15570165030542b47fef1fb3af5e04a069630f2475ded93c926b19d2c03860ac"},"schema_version":"1.0"},"canonical_sha256":"578a74ac6caccf84f9912f098309fd0c5a283de175e7f9f7dfe21cda5dbd2609","source":{"kind":"arxiv","id":"1209.6532","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.6532","created_at":"2026-05-18T03:44:25Z"},{"alias_kind":"arxiv_version","alias_value":"1209.6532v1","created_at":"2026-05-18T03:44:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.6532","created_at":"2026-05-18T03:44:25Z"},{"alias_kind":"pith_short_12","alias_value":"K6FHJLDMVTHY","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"K6FHJLDMVTHYJ6MR","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"K6FHJLDM","created_at":"2026-05-18T12:27:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:K6FHJLDMVTHYJ6MRF4EYGCP5BR","target":"record","payload":{"canonical_record":{"source":{"id":"1209.6532","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-09-28T14:23:57Z","cross_cats_sorted":[],"title_canon_sha256":"fc85b96f1a0b3face4df68c285db90b3d40df17e64bf27a641ae8ff2411352d6","abstract_canon_sha256":"15570165030542b47fef1fb3af5e04a069630f2475ded93c926b19d2c03860ac"},"schema_version":"1.0"},"canonical_sha256":"578a74ac6caccf84f9912f098309fd0c5a283de175e7f9f7dfe21cda5dbd2609","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:44:25.214941Z","signature_b64":"3PjNTkjajOLxRkywNtt4Lk3sXTNJG0D67iElXOYEvq9QZeDdtQTVk9z+nedSx6yuk1p1xZezdoieFHc74MbWAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"578a74ac6caccf84f9912f098309fd0c5a283de175e7f9f7dfe21cda5dbd2609","last_reissued_at":"2026-05-18T03:44:25.214282Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:44:25.214282Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.6532","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":"2026-05-18T03:44:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PCYOssBVfdiiR3NRV5lW5h8QkuHQ00C7OzWA/jnzoKaBzqvQESZhO5r0R6RHL2TkiNAF5zubsArRT0jAf3sNBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T23:23:19.469274Z"},"content_sha256":"ba1db2207c9876c87bb7bb2a2b8e9e38b1308a84be7490a36e6191cac7a5eae3","schema_version":"1.0","event_id":"sha256:ba1db2207c9876c87bb7bb2a2b8e9e38b1308a84be7490a36e6191cac7a5eae3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:K6FHJLDMVTHYJ6MRF4EYGCP5BR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On knots and links in lens spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Alessia Cattabriga, Enrico Manfredi, Michele Mulazzani","submitted_at":"2012-09-28T14:23:57Z","abstract_excerpt":"In this paper we study some aspects of knots and links in lens spaces. Namely, if we consider lens spaces as quotient of the unit ball $B^{3}$ with suitable identification of boundary points, then we can project the links on the equatorial disk of $B^{3}$, obtaining a regular diagram for them. In this contest, we obtain a complete finite set of Reidemeister type moves establishing equivalence, up to ambient isotopy, a Wirtinger type presentation for the fundamental group of the complement of the link and a diagrammatic method giving the first homology group. We also compute Alexander polynomia"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.6532","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":"2026-05-18T03:44:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mEsZyGioO1cwemDqKruxa1oCEU4W6QOatraqF57dhkbpd02AOeywPXhFVQcnYo3w4PIgVKviIUAex1mH1CsKAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T23:23:19.469638Z"},"content_sha256":"51c7d8646fd49138dbeea0408c68f8be8a91c09c66e0f3e0c912a90f8e0955b9","schema_version":"1.0","event_id":"sha256:51c7d8646fd49138dbeea0408c68f8be8a91c09c66e0f3e0c912a90f8e0955b9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K6FHJLDMVTHYJ6MRF4EYGCP5BR/bundle.json","state_url":"https://pith.science/pith/K6FHJLDMVTHYJ6MRF4EYGCP5BR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K6FHJLDMVTHYJ6MRF4EYGCP5BR/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":"2026-06-25T23:23:19Z","links":{"resolver":"https://pith.science/pith/K6FHJLDMVTHYJ6MRF4EYGCP5BR","bundle":"https://pith.science/pith/K6FHJLDMVTHYJ6MRF4EYGCP5BR/bundle.json","state":"https://pith.science/pith/K6FHJLDMVTHYJ6MRF4EYGCP5BR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K6FHJLDMVTHYJ6MRF4EYGCP5BR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:K6FHJLDMVTHYJ6MRF4EYGCP5BR","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":"15570165030542b47fef1fb3af5e04a069630f2475ded93c926b19d2c03860ac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-09-28T14:23:57Z","title_canon_sha256":"fc85b96f1a0b3face4df68c285db90b3d40df17e64bf27a641ae8ff2411352d6"},"schema_version":"1.0","source":{"id":"1209.6532","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.6532","created_at":"2026-05-18T03:44:25Z"},{"alias_kind":"arxiv_version","alias_value":"1209.6532v1","created_at":"2026-05-18T03:44:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.6532","created_at":"2026-05-18T03:44:25Z"},{"alias_kind":"pith_short_12","alias_value":"K6FHJLDMVTHY","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"K6FHJLDMVTHYJ6MR","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"K6FHJLDM","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:51c7d8646fd49138dbeea0408c68f8be8a91c09c66e0f3e0c912a90f8e0955b9","target":"graph","created_at":"2026-05-18T03:44:25Z","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":"In this paper we study some aspects of knots and links in lens spaces. Namely, if we consider lens spaces as quotient of the unit ball $B^{3}$ with suitable identification of boundary points, then we can project the links on the equatorial disk of $B^{3}$, obtaining a regular diagram for them. In this contest, we obtain a complete finite set of Reidemeister type moves establishing equivalence, up to ambient isotopy, a Wirtinger type presentation for the fundamental group of the complement of the link and a diagrammatic method giving the first homology group. We also compute Alexander polynomia","authors_text":"Alessia Cattabriga, Enrico Manfredi, Michele Mulazzani","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-09-28T14:23:57Z","title":"On knots and links in lens spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.6532","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:ba1db2207c9876c87bb7bb2a2b8e9e38b1308a84be7490a36e6191cac7a5eae3","target":"record","created_at":"2026-05-18T03:44:25Z","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":"15570165030542b47fef1fb3af5e04a069630f2475ded93c926b19d2c03860ac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-09-28T14:23:57Z","title_canon_sha256":"fc85b96f1a0b3face4df68c285db90b3d40df17e64bf27a641ae8ff2411352d6"},"schema_version":"1.0","source":{"id":"1209.6532","kind":"arxiv","version":1}},"canonical_sha256":"578a74ac6caccf84f9912f098309fd0c5a283de175e7f9f7dfe21cda5dbd2609","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"578a74ac6caccf84f9912f098309fd0c5a283de175e7f9f7dfe21cda5dbd2609","first_computed_at":"2026-05-18T03:44:25.214282Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:44:25.214282Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3PjNTkjajOLxRkywNtt4Lk3sXTNJG0D67iElXOYEvq9QZeDdtQTVk9z+nedSx6yuk1p1xZezdoieFHc74MbWAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:44:25.214941Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.6532","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba1db2207c9876c87bb7bb2a2b8e9e38b1308a84be7490a36e6191cac7a5eae3","sha256:51c7d8646fd49138dbeea0408c68f8be8a91c09c66e0f3e0c912a90f8e0955b9"],"state_sha256":"ce592a020728bbd1c7168ab6164c8c96e89051d04637b0790bd3e0f4c4ead0a7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+tI16piyW6a+lnOof7NTY9bFQErjg3CkGdTa1Q+F78Fge2kdAClVH9ZUQg/PbZWQYf35kTQRJ9lTEysimau8Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T23:23:19.471666Z","bundle_sha256":"0aa9352f5c721638d75b888695d9ddfd7a8b22f1002fddedea014055cc7109bd"}}