{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:INLK5UEIX45N643HX7TYZ7PVGY","short_pith_number":"pith:INLK5UEI","canonical_record":{"source":{"id":"1708.03925","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-08-13T16:19:28Z","cross_cats_sorted":[],"title_canon_sha256":"db93bd0d6bf4e95abb47f21c13905884acdd8c27487d3a1e03d5cf974417ec53","abstract_canon_sha256":"498b556431f4f5c803e503536ce6ed7f6840631f6f3c3af27d7bd4a123a2f399"},"schema_version":"1.0"},"canonical_sha256":"4356aed088bf3adf7367bfe78cfdf5362076df748be6ca596dadc8c4c8e65258","source":{"kind":"arxiv","id":"1708.03925","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.03925","created_at":"2026-05-18T00:38:07Z"},{"alias_kind":"arxiv_version","alias_value":"1708.03925v1","created_at":"2026-05-18T00:38:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.03925","created_at":"2026-05-18T00:38:07Z"},{"alias_kind":"pith_short_12","alias_value":"INLK5UEIX45N","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"INLK5UEIX45N643H","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"INLK5UEI","created_at":"2026-05-18T12:31:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:INLK5UEIX45N643HX7TYZ7PVGY","target":"record","payload":{"canonical_record":{"source":{"id":"1708.03925","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-08-13T16:19:28Z","cross_cats_sorted":[],"title_canon_sha256":"db93bd0d6bf4e95abb47f21c13905884acdd8c27487d3a1e03d5cf974417ec53","abstract_canon_sha256":"498b556431f4f5c803e503536ce6ed7f6840631f6f3c3af27d7bd4a123a2f399"},"schema_version":"1.0"},"canonical_sha256":"4356aed088bf3adf7367bfe78cfdf5362076df748be6ca596dadc8c4c8e65258","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:07.496754Z","signature_b64":"XXNYl4FvM8/pCZNzomLHd+lc/qLERnhgWQEP1zE1cThAjww/BmgHsTn8dcDkbeUFqEedZyh1Uow0an9r7dnxCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4356aed088bf3adf7367bfe78cfdf5362076df748be6ca596dadc8c4c8e65258","last_reissued_at":"2026-05-18T00:38:07.496247Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:07.496247Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.03925","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":"2026-05-18T00:38:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fouNH0nRkVi8KLEUhzX7DQymAvNqglfUh3D/iINXqNAL3RuW79M7joeFsbtnbzkf1MeK1IN3o3kLXKqHn2wECg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T06:12:43.763793Z"},"content_sha256":"979a88cd1884c48a10eaa68abf4772ea7693d5de7d8927567ab022ee02573b8a","schema_version":"1.0","event_id":"sha256:979a88cd1884c48a10eaa68abf4772ea7693d5de7d8927567ab022ee02573b8a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:INLK5UEIX45N643HX7TYZ7PVGY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"More intrinsically knotted graphs with 22 edges and the restoring method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Hyoungjun Kim, Seungsang Oh, Thomas Mattman","submitted_at":"2017-08-13T16:19:28Z","abstract_excerpt":"A graph is called intrinsically knotted if every embedding of the graph contains a knotted cycle. Johnson, Kidwell and Michael, and, independently, Mattman showed that intrinsically knotted graphs have at least 21 edges. Recently Lee, Kim, Lee and Oh, and, independently, Barsotti and Mattman, showed that $K_7$ and the 13 graphs obtained from $K_7$ by $\\nabla Y$ moves are the only intrinsically knotted graphs with 21 edges. Also Kim, Lee, Lee, Mattman and Oh showed that there are exactly three triangle-free intrinsically knotted graphs with 22 edges having at least two vertices of degree 5. Fur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.03925","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":"2026-05-18T00:38:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CQ56YoxPFIAmbUEyvAgSVelSQ7mBiAe4fhotWdPImSiaAtbbvjUirT+FvnmxUqh1pZu3ZRknfikxDfD1/MBhAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T06:12:43.764390Z"},"content_sha256":"17fdd8a917204dcff7102de797123f4a316b9033a955f35a421cf81e006865c1","schema_version":"1.0","event_id":"sha256:17fdd8a917204dcff7102de797123f4a316b9033a955f35a421cf81e006865c1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/INLK5UEIX45N643HX7TYZ7PVGY/bundle.json","state_url":"https://pith.science/pith/INLK5UEIX45N643HX7TYZ7PVGY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/INLK5UEIX45N643HX7TYZ7PVGY/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":"2026-05-21T06:12:43Z","links":{"resolver":"https://pith.science/pith/INLK5UEIX45N643HX7TYZ7PVGY","bundle":"https://pith.science/pith/INLK5UEIX45N643HX7TYZ7PVGY/bundle.json","state":"https://pith.science/pith/INLK5UEIX45N643HX7TYZ7PVGY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/INLK5UEIX45N643HX7TYZ7PVGY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:INLK5UEIX45N643HX7TYZ7PVGY","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":"498b556431f4f5c803e503536ce6ed7f6840631f6f3c3af27d7bd4a123a2f399","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-08-13T16:19:28Z","title_canon_sha256":"db93bd0d6bf4e95abb47f21c13905884acdd8c27487d3a1e03d5cf974417ec53"},"schema_version":"1.0","source":{"id":"1708.03925","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.03925","created_at":"2026-05-18T00:38:07Z"},{"alias_kind":"arxiv_version","alias_value":"1708.03925v1","created_at":"2026-05-18T00:38:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.03925","created_at":"2026-05-18T00:38:07Z"},{"alias_kind":"pith_short_12","alias_value":"INLK5UEIX45N","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"INLK5UEIX45N643H","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"INLK5UEI","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:17fdd8a917204dcff7102de797123f4a316b9033a955f35a421cf81e006865c1","target":"graph","created_at":"2026-05-18T00:38:07Z","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":"A graph is called intrinsically knotted if every embedding of the graph contains a knotted cycle. Johnson, Kidwell and Michael, and, independently, Mattman showed that intrinsically knotted graphs have at least 21 edges. Recently Lee, Kim, Lee and Oh, and, independently, Barsotti and Mattman, showed that $K_7$ and the 13 graphs obtained from $K_7$ by $\\nabla Y$ moves are the only intrinsically knotted graphs with 21 edges. Also Kim, Lee, Lee, Mattman and Oh showed that there are exactly three triangle-free intrinsically knotted graphs with 22 edges having at least two vertices of degree 5. Fur","authors_text":"Hyoungjun Kim, Seungsang Oh, Thomas Mattman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-08-13T16:19:28Z","title":"More intrinsically knotted graphs with 22 edges and the restoring method"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.03925","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":"sha256:979a88cd1884c48a10eaa68abf4772ea7693d5de7d8927567ab022ee02573b8a","target":"record","created_at":"2026-05-18T00:38:07Z","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":"498b556431f4f5c803e503536ce6ed7f6840631f6f3c3af27d7bd4a123a2f399","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-08-13T16:19:28Z","title_canon_sha256":"db93bd0d6bf4e95abb47f21c13905884acdd8c27487d3a1e03d5cf974417ec53"},"schema_version":"1.0","source":{"id":"1708.03925","kind":"arxiv","version":1}},"canonical_sha256":"4356aed088bf3adf7367bfe78cfdf5362076df748be6ca596dadc8c4c8e65258","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4356aed088bf3adf7367bfe78cfdf5362076df748be6ca596dadc8c4c8e65258","first_computed_at":"2026-05-18T00:38:07.496247Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:38:07.496247Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XXNYl4FvM8/pCZNzomLHd+lc/qLERnhgWQEP1zE1cThAjww/BmgHsTn8dcDkbeUFqEedZyh1Uow0an9r7dnxCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:38:07.496754Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.03925","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:979a88cd1884c48a10eaa68abf4772ea7693d5de7d8927567ab022ee02573b8a","sha256:17fdd8a917204dcff7102de797123f4a316b9033a955f35a421cf81e006865c1"],"state_sha256":"a3159c6d1d4d0045f75f0daba9122b344681f18426f5876efef5945f8f8d2eba"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xlFKuMis4qt27ZZq1PciQ6ZPZEvBDuTZjd/IyEmOCgX6W9X0j0MUeTxdR7J8jj7X2M9B1ETzR3kc+3Z8tqeBAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-21T06:12:43.766484Z","bundle_sha256":"529d9ce597735fefab651f6a8927ddeba7c8587b9f653bd24462085d0acc4cf8"}}