{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:4BAR4DURAM4BI3RN27Y3XRGXDH","short_pith_number":"pith:4BAR4DUR","canonical_record":{"source":{"id":"1703.07540","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-03-22T06:33:36Z","cross_cats_sorted":[],"title_canon_sha256":"4c3a91b2b9b4fca430c88b4953e6cb33510a76ddfea47eb04b98243a3145d9f1","abstract_canon_sha256":"10c60d3038ecc68874902278dbffadd470253c408ce3a6dce2c30c27f7ad10ce"},"schema_version":"1.0"},"canonical_sha256":"e0411e0e910338146e2dd7f1bbc4d719db194f3a361b7024ee5ffa749a04a538","source":{"kind":"arxiv","id":"1703.07540","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.07540","created_at":"2026-05-17T23:55:01Z"},{"alias_kind":"arxiv_version","alias_value":"1703.07540v3","created_at":"2026-05-17T23:55:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.07540","created_at":"2026-05-17T23:55:01Z"},{"alias_kind":"pith_short_12","alias_value":"4BAR4DURAM4B","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"4BAR4DURAM4BI3RN","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"4BAR4DUR","created_at":"2026-05-18T12:30:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:4BAR4DURAM4BI3RN27Y3XRGXDH","target":"record","payload":{"canonical_record":{"source":{"id":"1703.07540","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-03-22T06:33:36Z","cross_cats_sorted":[],"title_canon_sha256":"4c3a91b2b9b4fca430c88b4953e6cb33510a76ddfea47eb04b98243a3145d9f1","abstract_canon_sha256":"10c60d3038ecc68874902278dbffadd470253c408ce3a6dce2c30c27f7ad10ce"},"schema_version":"1.0"},"canonical_sha256":"e0411e0e910338146e2dd7f1bbc4d719db194f3a361b7024ee5ffa749a04a538","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:01.276469Z","signature_b64":"QLX7fgjRRGnzC1uM2VOm0KAEAJEiOMXqinvcDaIFMyNptiLwMcAh1Ksl2izULq7IP8psTBh9J0eSOv5ve0udDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e0411e0e910338146e2dd7f1bbc4d719db194f3a361b7024ee5ffa749a04a538","last_reissued_at":"2026-05-17T23:55:01.276058Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:01.276058Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.07540","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":"2026-05-17T23:55:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yKu4p+PGYy+1XOgfac0/QLd0IP1VJmVb+Xh/t6/Ix6oPhIryKG4I36jJ8VWwoIGIL3QY2kWEHAidFDpPVLMJAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T06:50:06.217388Z"},"content_sha256":"763bcbe2f9070449f2e644ac378c0c1aab746b80400f4da19e4a9a3689a3d470","schema_version":"1.0","event_id":"sha256:763bcbe2f9070449f2e644ac378c0c1aab746b80400f4da19e4a9a3689a3d470"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:4BAR4DURAM4BI3RN27Y3XRGXDH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multivariable signatures, genus bounds and $0.5$-solvable cobordisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Anthony Conway, Enrico Toffoli, Matthias Nagel","submitted_at":"2017-03-22T06:33:36Z","abstract_excerpt":"We refine prior bounds on how the multivariable signature and the nullity of a link change under link cobordisms. The formula generalizes a series of results about the 4-genus having their origins in the Murasugi-Tristram inequality, and at the same time extends previously known results about concordance invariance of the signature to a bigger set of allowed variables. Finally, we show that the multivariable signature and nullity are also invariant under $0.5$-solvable cobordism."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.07540","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":""},"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":"2026-05-17T23:55:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MJKqCBFS9Q4lcu+2+SSqwYjnhxHac8Xgb9GyEscfoty4xyck9e5gNQzbymVweiTD7Dufoe5XiFBLuiJPMOFnAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T06:50:06.218044Z"},"content_sha256":"cccba4d42d1bf2aacb028b2b8a1eadfe91c02cdae8a81b825f4abeab073771cc","schema_version":"1.0","event_id":"sha256:cccba4d42d1bf2aacb028b2b8a1eadfe91c02cdae8a81b825f4abeab073771cc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4BAR4DURAM4BI3RN27Y3XRGXDH/bundle.json","state_url":"https://pith.science/pith/4BAR4DURAM4BI3RN27Y3XRGXDH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4BAR4DURAM4BI3RN27Y3XRGXDH/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":"2026-06-04T06:50:06Z","links":{"resolver":"https://pith.science/pith/4BAR4DURAM4BI3RN27Y3XRGXDH","bundle":"https://pith.science/pith/4BAR4DURAM4BI3RN27Y3XRGXDH/bundle.json","state":"https://pith.science/pith/4BAR4DURAM4BI3RN27Y3XRGXDH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4BAR4DURAM4BI3RN27Y3XRGXDH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:4BAR4DURAM4BI3RN27Y3XRGXDH","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":"10c60d3038ecc68874902278dbffadd470253c408ce3a6dce2c30c27f7ad10ce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-03-22T06:33:36Z","title_canon_sha256":"4c3a91b2b9b4fca430c88b4953e6cb33510a76ddfea47eb04b98243a3145d9f1"},"schema_version":"1.0","source":{"id":"1703.07540","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.07540","created_at":"2026-05-17T23:55:01Z"},{"alias_kind":"arxiv_version","alias_value":"1703.07540v3","created_at":"2026-05-17T23:55:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.07540","created_at":"2026-05-17T23:55:01Z"},{"alias_kind":"pith_short_12","alias_value":"4BAR4DURAM4B","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"4BAR4DURAM4BI3RN","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"4BAR4DUR","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:cccba4d42d1bf2aacb028b2b8a1eadfe91c02cdae8a81b825f4abeab073771cc","target":"graph","created_at":"2026-05-17T23:55:01Z","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 refine prior bounds on how the multivariable signature and the nullity of a link change under link cobordisms. The formula generalizes a series of results about the 4-genus having their origins in the Murasugi-Tristram inequality, and at the same time extends previously known results about concordance invariance of the signature to a bigger set of allowed variables. Finally, we show that the multivariable signature and nullity are also invariant under $0.5$-solvable cobordism.","authors_text":"Anthony Conway, Enrico Toffoli, Matthias Nagel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-03-22T06:33:36Z","title":"Multivariable signatures, genus bounds and $0.5$-solvable cobordisms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.07540","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":"sha256:763bcbe2f9070449f2e644ac378c0c1aab746b80400f4da19e4a9a3689a3d470","target":"record","created_at":"2026-05-17T23:55:01Z","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":"10c60d3038ecc68874902278dbffadd470253c408ce3a6dce2c30c27f7ad10ce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-03-22T06:33:36Z","title_canon_sha256":"4c3a91b2b9b4fca430c88b4953e6cb33510a76ddfea47eb04b98243a3145d9f1"},"schema_version":"1.0","source":{"id":"1703.07540","kind":"arxiv","version":3}},"canonical_sha256":"e0411e0e910338146e2dd7f1bbc4d719db194f3a361b7024ee5ffa749a04a538","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e0411e0e910338146e2dd7f1bbc4d719db194f3a361b7024ee5ffa749a04a538","first_computed_at":"2026-05-17T23:55:01.276058Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:01.276058Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QLX7fgjRRGnzC1uM2VOm0KAEAJEiOMXqinvcDaIFMyNptiLwMcAh1Ksl2izULq7IP8psTBh9J0eSOv5ve0udDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:01.276469Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.07540","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:763bcbe2f9070449f2e644ac378c0c1aab746b80400f4da19e4a9a3689a3d470","sha256:cccba4d42d1bf2aacb028b2b8a1eadfe91c02cdae8a81b825f4abeab073771cc"],"state_sha256":"3043789c395d0f7f945028ea5db87a5b0f478e04bd419167394bfccba150b68e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9DPeBFzOl/YXaZHQlhGgj5yiCOqq6WveWBIcT3YDb9AGa51d3tS6bxbV14x5+u/LWxShPCxzEBovWl6qmLKpCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T06:50:06.221471Z","bundle_sha256":"c698e3b2a19288a09b9d82da8501bda0ecdb5171e2c178001ef1d0483ce14f2c"}}