{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:AQRVDHH3XEIJDMQ45IOAE2PYHL","short_pith_number":"pith:AQRVDHH3","canonical_record":{"source":{"id":"1707.05585","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-07-18T12:29:27Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"dd6a0a6e08a1843533e9d6872f7479077f30dc3709771649fdc40fce55809352","abstract_canon_sha256":"56ad181f2c077ead1b84d01a0c71caeafa857c55dbafc7514d9b5bd5887dee70"},"schema_version":"1.0"},"canonical_sha256":"0423519cfbb91091b21cea1c0269f83ac2b4dcd3694a640f762534f2083e61ff","source":{"kind":"arxiv","id":"1707.05585","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.05585","created_at":"2026-05-18T00:40:01Z"},{"alias_kind":"arxiv_version","alias_value":"1707.05585v1","created_at":"2026-05-18T00:40:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.05585","created_at":"2026-05-18T00:40:01Z"},{"alias_kind":"pith_short_12","alias_value":"AQRVDHH3XEIJ","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"AQRVDHH3XEIJDMQ4","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"AQRVDHH3","created_at":"2026-05-18T12:31:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:AQRVDHH3XEIJDMQ45IOAE2PYHL","target":"record","payload":{"canonical_record":{"source":{"id":"1707.05585","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-07-18T12:29:27Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"dd6a0a6e08a1843533e9d6872f7479077f30dc3709771649fdc40fce55809352","abstract_canon_sha256":"56ad181f2c077ead1b84d01a0c71caeafa857c55dbafc7514d9b5bd5887dee70"},"schema_version":"1.0"},"canonical_sha256":"0423519cfbb91091b21cea1c0269f83ac2b4dcd3694a640f762534f2083e61ff","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:01.962442Z","signature_b64":"fuypew32uVkk0DYIdYynnwMbYnkq0DL9rTZT+8+40hJfMPvMq1t03Qu831Zj2wxp5W6AaWS1CU/Sdk+jWhQVCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0423519cfbb91091b21cea1c0269f83ac2b4dcd3694a640f762534f2083e61ff","last_reissued_at":"2026-05-18T00:40:01.961951Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:01.961951Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.05585","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":"2026-05-18T00:40:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gQp0shGp4rSBA2JEeWGVamnPNT+RlRKY2dsDzECPljRlglPeKZATMvBjfOIvM/MfZfdYp8OYIBNPRU2nxsaIDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T22:35:09.674567Z"},"content_sha256":"18cdc289250a9b98052ce393de4e52dc27e90d1a3bc80b16daa4f7e9eb4e9399","schema_version":"1.0","event_id":"sha256:18cdc289250a9b98052ce393de4e52dc27e90d1a3bc80b16daa4f7e9eb4e9399"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:AQRVDHH3XEIJDMQ45IOAE2PYHL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A polynomial invariant for plane curve complements: Krammer polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.AG","authors_text":"Hubeyb Gurdogan, Mehmet Emin Aktas, Serdar Cellat","submitted_at":"2017-07-18T12:29:27Z","abstract_excerpt":"We use the Krammer representation of the braid group in Libgober's invariant and construct a new multivariate polynomial invariant for curve complements: Krammer polynomial. We show that the Krammer polynomial of an essential braid is equal to zero. We also compute the Krammer polynomials of some certain n-gonal curves."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.05585","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":"2026-05-18T00:40:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RaJZffYOT9kGbqm/4GJ2FqG11eh01O6y/cNEnQw/Wg0Xw18pO1ff3tibgPx5jWJhPxoDfAggnoJqDeIYSPtCBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T22:35:09.675257Z"},"content_sha256":"3fb2163134f293bdb7ad45e1d6aafbf3389d683bba653caf38ff38d18e435848","schema_version":"1.0","event_id":"sha256:3fb2163134f293bdb7ad45e1d6aafbf3389d683bba653caf38ff38d18e435848"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AQRVDHH3XEIJDMQ45IOAE2PYHL/bundle.json","state_url":"https://pith.science/pith/AQRVDHH3XEIJDMQ45IOAE2PYHL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AQRVDHH3XEIJDMQ45IOAE2PYHL/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":"2026-05-26T22:35:09Z","links":{"resolver":"https://pith.science/pith/AQRVDHH3XEIJDMQ45IOAE2PYHL","bundle":"https://pith.science/pith/AQRVDHH3XEIJDMQ45IOAE2PYHL/bundle.json","state":"https://pith.science/pith/AQRVDHH3XEIJDMQ45IOAE2PYHL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AQRVDHH3XEIJDMQ45IOAE2PYHL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:AQRVDHH3XEIJDMQ45IOAE2PYHL","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":"56ad181f2c077ead1b84d01a0c71caeafa857c55dbafc7514d9b5bd5887dee70","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-07-18T12:29:27Z","title_canon_sha256":"dd6a0a6e08a1843533e9d6872f7479077f30dc3709771649fdc40fce55809352"},"schema_version":"1.0","source":{"id":"1707.05585","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.05585","created_at":"2026-05-18T00:40:01Z"},{"alias_kind":"arxiv_version","alias_value":"1707.05585v1","created_at":"2026-05-18T00:40:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.05585","created_at":"2026-05-18T00:40:01Z"},{"alias_kind":"pith_short_12","alias_value":"AQRVDHH3XEIJ","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"AQRVDHH3XEIJDMQ4","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"AQRVDHH3","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:3fb2163134f293bdb7ad45e1d6aafbf3389d683bba653caf38ff38d18e435848","target":"graph","created_at":"2026-05-18T00:40:01Z","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 use the Krammer representation of the braid group in Libgober's invariant and construct a new multivariate polynomial invariant for curve complements: Krammer polynomial. We show that the Krammer polynomial of an essential braid is equal to zero. We also compute the Krammer polynomials of some certain n-gonal curves.","authors_text":"Hubeyb Gurdogan, Mehmet Emin Aktas, Serdar Cellat","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-07-18T12:29:27Z","title":"A polynomial invariant for plane curve complements: Krammer polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.05585","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":"sha256:18cdc289250a9b98052ce393de4e52dc27e90d1a3bc80b16daa4f7e9eb4e9399","target":"record","created_at":"2026-05-18T00:40:01Z","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":"56ad181f2c077ead1b84d01a0c71caeafa857c55dbafc7514d9b5bd5887dee70","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-07-18T12:29:27Z","title_canon_sha256":"dd6a0a6e08a1843533e9d6872f7479077f30dc3709771649fdc40fce55809352"},"schema_version":"1.0","source":{"id":"1707.05585","kind":"arxiv","version":1}},"canonical_sha256":"0423519cfbb91091b21cea1c0269f83ac2b4dcd3694a640f762534f2083e61ff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0423519cfbb91091b21cea1c0269f83ac2b4dcd3694a640f762534f2083e61ff","first_computed_at":"2026-05-18T00:40:01.961951Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:01.961951Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fuypew32uVkk0DYIdYynnwMbYnkq0DL9rTZT+8+40hJfMPvMq1t03Qu831Zj2wxp5W6AaWS1CU/Sdk+jWhQVCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:01.962442Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.05585","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:18cdc289250a9b98052ce393de4e52dc27e90d1a3bc80b16daa4f7e9eb4e9399","sha256:3fb2163134f293bdb7ad45e1d6aafbf3389d683bba653caf38ff38d18e435848"],"state_sha256":"afe126dd57c59abd49d54a96398c27803bfc541f5c37cc4cbe7ea8721080b6d9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ht4616iw8QM7jnK1PWVE3LYThyF7PbKo7Ugpjo0MsRmuazYYExyobuMc9CWI4+UvCuzwgt40h1p/6sX4fWDQBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T22:35:09.678036Z","bundle_sha256":"95e5a07ead79350ef7fe523ef80f3bfe8d83dcb6b5f5efbd41d83733513c70f6"}}