{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:ZF5DYCPSQVXBRJ7QAGXNQYF6DV","short_pith_number":"pith:ZF5DYCPS","canonical_record":{"source":{"id":"1501.00580","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-01-03T17:14:41Z","cross_cats_sorted":[],"title_canon_sha256":"b55a0c5ff3d351567200ed687897f883430894c6d5da79eeaaeefda168189d86","abstract_canon_sha256":"66643d3e7fdb7896c1385e2c27e058af0f281d81a203c9507c13ab3764579e29"},"schema_version":"1.0"},"canonical_sha256":"c97a3c09f2856e18a7f001aed860be1d4a11d14d7eca24792f595d543841e4be","source":{"kind":"arxiv","id":"1501.00580","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.00580","created_at":"2026-05-18T02:28:13Z"},{"alias_kind":"arxiv_version","alias_value":"1501.00580v2","created_at":"2026-05-18T02:28:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.00580","created_at":"2026-05-18T02:28:13Z"},{"alias_kind":"pith_short_12","alias_value":"ZF5DYCPSQVXB","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZF5DYCPSQVXBRJ7Q","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZF5DYCPS","created_at":"2026-05-18T12:29:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:ZF5DYCPSQVXBRJ7QAGXNQYF6DV","target":"record","payload":{"canonical_record":{"source":{"id":"1501.00580","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-01-03T17:14:41Z","cross_cats_sorted":[],"title_canon_sha256":"b55a0c5ff3d351567200ed687897f883430894c6d5da79eeaaeefda168189d86","abstract_canon_sha256":"66643d3e7fdb7896c1385e2c27e058af0f281d81a203c9507c13ab3764579e29"},"schema_version":"1.0"},"canonical_sha256":"c97a3c09f2856e18a7f001aed860be1d4a11d14d7eca24792f595d543841e4be","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:13.112031Z","signature_b64":"Kvg1OOdJo+NJVCo6nBKmq9x5pn3DOnuPnuX5ouQsBhKl+yI6s56WBtFa7yMDge7TCRqRb/Bl+KKt2r0/pBa6Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c97a3c09f2856e18a7f001aed860be1d4a11d14d7eca24792f595d543841e4be","last_reissued_at":"2026-05-18T02:28:13.111429Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:13.111429Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.00580","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":"2026-05-18T02:28:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a655o1B7tdNzJ7XKAwH52kxVaX3LL0Vn86zmbNp1pR9z8PeZohciRN4UsMvCDugSOCt6jIruCh9oJU5vUporBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T15:18:39.946171Z"},"content_sha256":"2200f2711dd7817a93b85cf82bf719f696b563e79520b80e114192ef4f49bda4","schema_version":"1.0","event_id":"sha256:2200f2711dd7817a93b85cf82bf719f696b563e79520b80e114192ef4f49bda4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:ZF5DYCPSQVXBRJ7QAGXNQYF6DV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"One-Term Parity Bracket For Braids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Vassily Olegovich Manturov","submitted_at":"2015-01-03T17:14:41Z","abstract_excerpt":"In previous papers, the author realized the following principle for many knot theories: if a knot diagram is complicated enough then it reproduces itself, i.e., is a subdiagram of any other diagram equivalent to it. This principle is realized by diagram-valued invariants [ ] of knots such that [K]=K. It turns out that in the case of free braids, the same principle can be realized an unexpectedly easy way by a one-term invariant formula."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.00580","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":"2026-05-18T02:28:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UeW0azwiQerdcnr1hYqMYZkLHjkmeGhUyc4ExH4+zqpK7DVieRFAPlKUJpbz6VibRFY8L6WGfAzJj6wnDVTZAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T15:18:39.946527Z"},"content_sha256":"57c587c26ad61dbef8a024193b4b8521d2db4c3ecf79f931b65e737124dd4221","schema_version":"1.0","event_id":"sha256:57c587c26ad61dbef8a024193b4b8521d2db4c3ecf79f931b65e737124dd4221"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZF5DYCPSQVXBRJ7QAGXNQYF6DV/bundle.json","state_url":"https://pith.science/pith/ZF5DYCPSQVXBRJ7QAGXNQYF6DV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZF5DYCPSQVXBRJ7QAGXNQYF6DV/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":"2026-06-03T15:18:39Z","links":{"resolver":"https://pith.science/pith/ZF5DYCPSQVXBRJ7QAGXNQYF6DV","bundle":"https://pith.science/pith/ZF5DYCPSQVXBRJ7QAGXNQYF6DV/bundle.json","state":"https://pith.science/pith/ZF5DYCPSQVXBRJ7QAGXNQYF6DV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZF5DYCPSQVXBRJ7QAGXNQYF6DV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ZF5DYCPSQVXBRJ7QAGXNQYF6DV","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":"66643d3e7fdb7896c1385e2c27e058af0f281d81a203c9507c13ab3764579e29","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-01-03T17:14:41Z","title_canon_sha256":"b55a0c5ff3d351567200ed687897f883430894c6d5da79eeaaeefda168189d86"},"schema_version":"1.0","source":{"id":"1501.00580","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.00580","created_at":"2026-05-18T02:28:13Z"},{"alias_kind":"arxiv_version","alias_value":"1501.00580v2","created_at":"2026-05-18T02:28:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.00580","created_at":"2026-05-18T02:28:13Z"},{"alias_kind":"pith_short_12","alias_value":"ZF5DYCPSQVXB","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZF5DYCPSQVXBRJ7Q","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZF5DYCPS","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:57c587c26ad61dbef8a024193b4b8521d2db4c3ecf79f931b65e737124dd4221","target":"graph","created_at":"2026-05-18T02:28:13Z","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 previous papers, the author realized the following principle for many knot theories: if a knot diagram is complicated enough then it reproduces itself, i.e., is a subdiagram of any other diagram equivalent to it. This principle is realized by diagram-valued invariants [ ] of knots such that [K]=K. It turns out that in the case of free braids, the same principle can be realized an unexpectedly easy way by a one-term invariant formula.","authors_text":"Vassily Olegovich Manturov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-01-03T17:14:41Z","title":"One-Term Parity Bracket For Braids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.00580","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":"sha256:2200f2711dd7817a93b85cf82bf719f696b563e79520b80e114192ef4f49bda4","target":"record","created_at":"2026-05-18T02:28:13Z","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":"66643d3e7fdb7896c1385e2c27e058af0f281d81a203c9507c13ab3764579e29","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-01-03T17:14:41Z","title_canon_sha256":"b55a0c5ff3d351567200ed687897f883430894c6d5da79eeaaeefda168189d86"},"schema_version":"1.0","source":{"id":"1501.00580","kind":"arxiv","version":2}},"canonical_sha256":"c97a3c09f2856e18a7f001aed860be1d4a11d14d7eca24792f595d543841e4be","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c97a3c09f2856e18a7f001aed860be1d4a11d14d7eca24792f595d543841e4be","first_computed_at":"2026-05-18T02:28:13.111429Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:13.111429Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Kvg1OOdJo+NJVCo6nBKmq9x5pn3DOnuPnuX5ouQsBhKl+yI6s56WBtFa7yMDge7TCRqRb/Bl+KKt2r0/pBa6Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:13.112031Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.00580","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2200f2711dd7817a93b85cf82bf719f696b563e79520b80e114192ef4f49bda4","sha256:57c587c26ad61dbef8a024193b4b8521d2db4c3ecf79f931b65e737124dd4221"],"state_sha256":"0b9ce994f7c9273f62680f92715f29648e746bf5d4617e3be52f8cab27218c14"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NqFpF0yHzIYC4Qsw2auQ6uN3dynu4ZjGufo7sEws+jBT+wczkQVF6F0KJHTnB25ORgKv8hJxNiotBhWhINWvCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T15:18:39.948423Z","bundle_sha256":"a9ebd9210a78f41ba73b8ab8e19232a1984f052b91a0780afebd05d50c889aa4"}}