{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:TG5AZZZEJZRBTEL6PFRPHBC3VY","short_pith_number":"pith:TG5AZZZE","canonical_record":{"source":{"id":"1511.07073","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-11-22T21:34:59Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"ad70642bcd4d50067ded11692d5277cf358c568abcfe55d0811a280120177500","abstract_canon_sha256":"44fc2bfed2c587ae86a76a00d01e15867cfef6ac236140821ad1ac968587a301"},"schema_version":"1.0"},"canonical_sha256":"99ba0ce7244e6219917e7962f3845bae263ec92890d0990038b170fcdb65c980","source":{"kind":"arxiv","id":"1511.07073","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.07073","created_at":"2026-05-18T01:26:16Z"},{"alias_kind":"arxiv_version","alias_value":"1511.07073v1","created_at":"2026-05-18T01:26:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.07073","created_at":"2026-05-18T01:26:16Z"},{"alias_kind":"pith_short_12","alias_value":"TG5AZZZEJZRB","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TG5AZZZEJZRBTEL6","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TG5AZZZE","created_at":"2026-05-18T12:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:TG5AZZZEJZRBTEL6PFRPHBC3VY","target":"record","payload":{"canonical_record":{"source":{"id":"1511.07073","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-11-22T21:34:59Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"ad70642bcd4d50067ded11692d5277cf358c568abcfe55d0811a280120177500","abstract_canon_sha256":"44fc2bfed2c587ae86a76a00d01e15867cfef6ac236140821ad1ac968587a301"},"schema_version":"1.0"},"canonical_sha256":"99ba0ce7244e6219917e7962f3845bae263ec92890d0990038b170fcdb65c980","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:26:16.737532Z","signature_b64":"zuF+lKFU4dSQDHHIL5djv5wf9SJ5LdIqen9YiR1vpcEnf52IP/KZO38Tt8PjdKVN2cripAEZAEJgGjIpRlyKCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"99ba0ce7244e6219917e7962f3845bae263ec92890d0990038b170fcdb65c980","last_reissued_at":"2026-05-18T01:26:16.736758Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:26:16.736758Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.07073","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":"2026-05-18T01:26:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YcWJeSupozfoPJt+reHHb7/yDK87lXT1be3y5KUDumIqoQw7GJ0TGA6l4PufGVWMeYL2FWPE90/534JP/sWEAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T09:26:32.108242Z"},"content_sha256":"879c7ff67408de6a67d624edef3f91eefb6172115074756142ea7f9e7188e49f","schema_version":"1.0","event_id":"sha256:879c7ff67408de6a67d624edef3f91eefb6172115074756142ea7f9e7188e49f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:TG5AZZZEJZRBTEL6PFRPHBC3VY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"1-domination of knots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.AT","authors_text":"Dale Rolfsen, Michel Boileau, Shicheng Wang, Steven Boyer","submitted_at":"2015-11-22T21:34:59Z","abstract_excerpt":"We say that a knot $k_1$ in the $3$-sphere {\\it $1$-dominates} another $k_2$ if there is a proper degree 1 map $E(k_1) \\to E(k_2)$ between their exteriors, and write $k_1 \\ge k_2$. When $k_1 \\ge k_2$ but $k_1 \\ne k_2$ we write $k_1 > k_2$. One expects in the latter eventuality that $k_1$ is more {\\it complicated}. In this paper we produce various sorts of evidence to support this philosophy."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.07073","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":"2026-05-18T01:26:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8SPsTPSSE115uT7vYDqg9+wPyuAtc6K8i1d99aRMUwZ7hx3n64r6peHfk7aErHtmKdBGnZRp9zzxVvitc7BABQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T09:26:32.108905Z"},"content_sha256":"d4eda1eeefc9ecbc1dbce103f145152d272cdad8e909182e7371e52cd9e54a8b","schema_version":"1.0","event_id":"sha256:d4eda1eeefc9ecbc1dbce103f145152d272cdad8e909182e7371e52cd9e54a8b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TG5AZZZEJZRBTEL6PFRPHBC3VY/bundle.json","state_url":"https://pith.science/pith/TG5AZZZEJZRBTEL6PFRPHBC3VY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TG5AZZZEJZRBTEL6PFRPHBC3VY/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":"2026-05-27T09:26:32Z","links":{"resolver":"https://pith.science/pith/TG5AZZZEJZRBTEL6PFRPHBC3VY","bundle":"https://pith.science/pith/TG5AZZZEJZRBTEL6PFRPHBC3VY/bundle.json","state":"https://pith.science/pith/TG5AZZZEJZRBTEL6PFRPHBC3VY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TG5AZZZEJZRBTEL6PFRPHBC3VY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:TG5AZZZEJZRBTEL6PFRPHBC3VY","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":"44fc2bfed2c587ae86a76a00d01e15867cfef6ac236140821ad1ac968587a301","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-11-22T21:34:59Z","title_canon_sha256":"ad70642bcd4d50067ded11692d5277cf358c568abcfe55d0811a280120177500"},"schema_version":"1.0","source":{"id":"1511.07073","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.07073","created_at":"2026-05-18T01:26:16Z"},{"alias_kind":"arxiv_version","alias_value":"1511.07073v1","created_at":"2026-05-18T01:26:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.07073","created_at":"2026-05-18T01:26:16Z"},{"alias_kind":"pith_short_12","alias_value":"TG5AZZZEJZRB","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TG5AZZZEJZRBTEL6","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TG5AZZZE","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:d4eda1eeefc9ecbc1dbce103f145152d272cdad8e909182e7371e52cd9e54a8b","target":"graph","created_at":"2026-05-18T01:26:16Z","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 say that a knot $k_1$ in the $3$-sphere {\\it $1$-dominates} another $k_2$ if there is a proper degree 1 map $E(k_1) \\to E(k_2)$ between their exteriors, and write $k_1 \\ge k_2$. When $k_1 \\ge k_2$ but $k_1 \\ne k_2$ we write $k_1 > k_2$. One expects in the latter eventuality that $k_1$ is more {\\it complicated}. In this paper we produce various sorts of evidence to support this philosophy.","authors_text":"Dale Rolfsen, Michel Boileau, Shicheng Wang, Steven Boyer","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-11-22T21:34:59Z","title":"1-domination of knots"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.07073","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":"sha256:879c7ff67408de6a67d624edef3f91eefb6172115074756142ea7f9e7188e49f","target":"record","created_at":"2026-05-18T01:26:16Z","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":"44fc2bfed2c587ae86a76a00d01e15867cfef6ac236140821ad1ac968587a301","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-11-22T21:34:59Z","title_canon_sha256":"ad70642bcd4d50067ded11692d5277cf358c568abcfe55d0811a280120177500"},"schema_version":"1.0","source":{"id":"1511.07073","kind":"arxiv","version":1}},"canonical_sha256":"99ba0ce7244e6219917e7962f3845bae263ec92890d0990038b170fcdb65c980","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"99ba0ce7244e6219917e7962f3845bae263ec92890d0990038b170fcdb65c980","first_computed_at":"2026-05-18T01:26:16.736758Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:26:16.736758Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zuF+lKFU4dSQDHHIL5djv5wf9SJ5LdIqen9YiR1vpcEnf52IP/KZO38Tt8PjdKVN2cripAEZAEJgGjIpRlyKCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:26:16.737532Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.07073","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:879c7ff67408de6a67d624edef3f91eefb6172115074756142ea7f9e7188e49f","sha256:d4eda1eeefc9ecbc1dbce103f145152d272cdad8e909182e7371e52cd9e54a8b"],"state_sha256":"adb16727da656541ddd88a0c47a3abeb09a6e86995e67425797d0c1f5d3f2361"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qDW3Ol73QHmIMV+PWG9KEsLc+uwlTLFCMzzYOoNsggaScEAWciX0Vzs0ltU6og97H22TMHpOKogDM43RkHhuAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T09:26:32.112454Z","bundle_sha256":"bd1ff9c5ce6ad15eb9397d75dc6ba7a56904cd6efd6ee8e5bf2a06707426f903"}}