{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:NIEJMNXZJZDNB64JOCRX2GBHUI","short_pith_number":"pith:NIEJMNXZ","canonical_record":{"source":{"id":"math/0702783","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GT","submitted_at":"2007-02-26T14:53:08Z","cross_cats_sorted":[],"title_canon_sha256":"045d3157210acab83834f15c94ff44571ea825ef86908a4382878e6714c95760","abstract_canon_sha256":"9eb96d496b264f464bfed72c2b224c77f63d87231dc87a1899999291539ef622"},"schema_version":"1.0"},"canonical_sha256":"6a089636f94e46d0fb8970a37d1827a21eb57f9df462966675fe8c4835116953","source":{"kind":"arxiv","id":"math/0702783","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0702783","created_at":"2026-05-18T02:57:45Z"},{"alias_kind":"arxiv_version","alias_value":"math/0702783v1","created_at":"2026-05-18T02:57:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0702783","created_at":"2026-05-18T02:57:45Z"},{"alias_kind":"pith_short_12","alias_value":"NIEJMNXZJZDN","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"NIEJMNXZJZDNB64J","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"NIEJMNXZ","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:NIEJMNXZJZDNB64JOCRX2GBHUI","target":"record","payload":{"canonical_record":{"source":{"id":"math/0702783","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GT","submitted_at":"2007-02-26T14:53:08Z","cross_cats_sorted":[],"title_canon_sha256":"045d3157210acab83834f15c94ff44571ea825ef86908a4382878e6714c95760","abstract_canon_sha256":"9eb96d496b264f464bfed72c2b224c77f63d87231dc87a1899999291539ef622"},"schema_version":"1.0"},"canonical_sha256":"6a089636f94e46d0fb8970a37d1827a21eb57f9df462966675fe8c4835116953","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:57:45.261325Z","signature_b64":"PvR+us/Liaep22Nau9PHl7Y2EQflI/6cxcKvMWuTNv+44038ujVTB3WrqjIlpclgT6eko9XTZZFmSyZH3+XHAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a089636f94e46d0fb8970a37d1827a21eb57f9df462966675fe8c4835116953","last_reissued_at":"2026-05-18T02:57:45.260784Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:57:45.260784Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0702783","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":"2026-05-18T02:57:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V8019Td+hjFdurpPMsGYaFNChSTlAZpxRKMJKbJ1gKzRqLKyGbq4hDGLW/4VCo2D1njeVBPYXzxo7pisOk9+Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T14:13:11.516032Z"},"content_sha256":"3b95b2756377f43e1890c187e34acf0dd80c6c69572dab650893e70495f2e283","schema_version":"1.0","event_id":"sha256:3b95b2756377f43e1890c187e34acf0dd80c6c69572dab650893e70495f2e283"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:NIEJMNXZJZDNB64JOCRX2GBHUI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On cyclic branched coverings of prime knots","license":"","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"L. Paoluzzi, M. Boileau","submitted_at":"2007-02-26T14:53:08Z","abstract_excerpt":"We prove that a prime knot K is not determined by its p-fold cyclic branched cover for at most two odd primes p. Moreover, we show that for a given odd prime p, the p-fold cyclic branched cover of a prime knot K is the p-fold cyclic branched cover of at most one more knot K' non equivalent to K. To prove the main theorem, a result concerning the symmetries of knots is also obtained. This latter result can be interpreted as a characterisation of the trivial knot."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0702783","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":"2026-05-18T02:57:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4nkceG3KNUwbjqJb7yqlOVplWsEqWzjgCRuMN7z4rnxeltN0+9uBX+3m0tZeb2v0BHibQlerBbdYoNb9BScGAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T14:13:11.516403Z"},"content_sha256":"e4c636fe780040e53341078cf54ba8e5af9b3345462a3b003a11cda619a30825","schema_version":"1.0","event_id":"sha256:e4c636fe780040e53341078cf54ba8e5af9b3345462a3b003a11cda619a30825"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NIEJMNXZJZDNB64JOCRX2GBHUI/bundle.json","state_url":"https://pith.science/pith/NIEJMNXZJZDNB64JOCRX2GBHUI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NIEJMNXZJZDNB64JOCRX2GBHUI/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":"2026-06-23T14:13:11Z","links":{"resolver":"https://pith.science/pith/NIEJMNXZJZDNB64JOCRX2GBHUI","bundle":"https://pith.science/pith/NIEJMNXZJZDNB64JOCRX2GBHUI/bundle.json","state":"https://pith.science/pith/NIEJMNXZJZDNB64JOCRX2GBHUI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NIEJMNXZJZDNB64JOCRX2GBHUI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:NIEJMNXZJZDNB64JOCRX2GBHUI","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":"9eb96d496b264f464bfed72c2b224c77f63d87231dc87a1899999291539ef622","cross_cats_sorted":[],"license":"","primary_cat":"math.GT","submitted_at":"2007-02-26T14:53:08Z","title_canon_sha256":"045d3157210acab83834f15c94ff44571ea825ef86908a4382878e6714c95760"},"schema_version":"1.0","source":{"id":"math/0702783","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0702783","created_at":"2026-05-18T02:57:45Z"},{"alias_kind":"arxiv_version","alias_value":"math/0702783v1","created_at":"2026-05-18T02:57:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0702783","created_at":"2026-05-18T02:57:45Z"},{"alias_kind":"pith_short_12","alias_value":"NIEJMNXZJZDN","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"NIEJMNXZJZDNB64J","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"NIEJMNXZ","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:e4c636fe780040e53341078cf54ba8e5af9b3345462a3b003a11cda619a30825","target":"graph","created_at":"2026-05-18T02:57:45Z","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 prove that a prime knot K is not determined by its p-fold cyclic branched cover for at most two odd primes p. Moreover, we show that for a given odd prime p, the p-fold cyclic branched cover of a prime knot K is the p-fold cyclic branched cover of at most one more knot K' non equivalent to K. To prove the main theorem, a result concerning the symmetries of knots is also obtained. This latter result can be interpreted as a characterisation of the trivial knot.","authors_text":"L. Paoluzzi, M. Boileau","cross_cats":[],"headline":"","license":"","primary_cat":"math.GT","submitted_at":"2007-02-26T14:53:08Z","title":"On cyclic branched coverings of prime knots"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0702783","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":"sha256:3b95b2756377f43e1890c187e34acf0dd80c6c69572dab650893e70495f2e283","target":"record","created_at":"2026-05-18T02:57:45Z","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":"9eb96d496b264f464bfed72c2b224c77f63d87231dc87a1899999291539ef622","cross_cats_sorted":[],"license":"","primary_cat":"math.GT","submitted_at":"2007-02-26T14:53:08Z","title_canon_sha256":"045d3157210acab83834f15c94ff44571ea825ef86908a4382878e6714c95760"},"schema_version":"1.0","source":{"id":"math/0702783","kind":"arxiv","version":1}},"canonical_sha256":"6a089636f94e46d0fb8970a37d1827a21eb57f9df462966675fe8c4835116953","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a089636f94e46d0fb8970a37d1827a21eb57f9df462966675fe8c4835116953","first_computed_at":"2026-05-18T02:57:45.260784Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:57:45.260784Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PvR+us/Liaep22Nau9PHl7Y2EQflI/6cxcKvMWuTNv+44038ujVTB3WrqjIlpclgT6eko9XTZZFmSyZH3+XHAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:57:45.261325Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0702783","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3b95b2756377f43e1890c187e34acf0dd80c6c69572dab650893e70495f2e283","sha256:e4c636fe780040e53341078cf54ba8e5af9b3345462a3b003a11cda619a30825"],"state_sha256":"ddef23cdacc3615f4ba59a710baf21e292ddd046526c17300c180075ba4c9bb1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ETV03jRJtV1qkaFd5J6bvfQYmz9I1ajUI+n4FYo0fj2GsV9gyeyW9gr3IGqZcl9KkVGW8y7X63X3hEmUFfHTBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T14:13:11.518471Z","bundle_sha256":"5e28ca4ce9818ce21cb82625da2af35c2b1bd120320a1ad5259476b3a166b405"}}