{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:M5STITKEVGKFL26IFWEVYPXHWG","short_pith_number":"pith:M5STITKE","canonical_record":{"source":{"id":"2009.03502","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2020-09-08T03:38:29Z","cross_cats_sorted":[],"title_canon_sha256":"d5a02ff5df5a694586957fa9125eda1352bd01d269e087fcf0d3ef50a10072bd","abstract_canon_sha256":"5e1f3bb52144821e2d9453badd2108f65dd9e852f68c8ca2a68381b3dd16dbd2"},"schema_version":"1.0"},"canonical_sha256":"6765344d44a99455ebc82d895c3ee7b19cb42a4bbcd49f1ab147d86abc66a76b","source":{"kind":"arxiv","id":"2009.03502","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2009.03502","created_at":"2026-07-05T03:43:37Z"},{"alias_kind":"arxiv_version","alias_value":"2009.03502v3","created_at":"2026-07-05T03:43:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2009.03502","created_at":"2026-07-05T03:43:37Z"},{"alias_kind":"pith_short_12","alias_value":"M5STITKEVGKF","created_at":"2026-07-05T03:43:37Z"},{"alias_kind":"pith_short_16","alias_value":"M5STITKEVGKFL26I","created_at":"2026-07-05T03:43:37Z"},{"alias_kind":"pith_short_8","alias_value":"M5STITKE","created_at":"2026-07-05T03:43:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:M5STITKEVGKFL26IFWEVYPXHWG","target":"record","payload":{"canonical_record":{"source":{"id":"2009.03502","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2020-09-08T03:38:29Z","cross_cats_sorted":[],"title_canon_sha256":"d5a02ff5df5a694586957fa9125eda1352bd01d269e087fcf0d3ef50a10072bd","abstract_canon_sha256":"5e1f3bb52144821e2d9453badd2108f65dd9e852f68c8ca2a68381b3dd16dbd2"},"schema_version":"1.0"},"canonical_sha256":"6765344d44a99455ebc82d895c3ee7b19cb42a4bbcd49f1ab147d86abc66a76b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:43:37.077734Z","signature_b64":"wV6fGZ/VaafAQZ3eh7dmw2mT7y0vLVjWXo94+YHfqvD6HySYTywAWn78tglgm19FBQHWXh7/oNsF6T7TU5YGCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6765344d44a99455ebc82d895c3ee7b19cb42a4bbcd49f1ab147d86abc66a76b","last_reissued_at":"2026-07-05T03:43:37.077235Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:43:37.077235Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2009.03502","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":"2026-07-05T03:43:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iEGVE/YzxlzobE5JnWrO4oqWxNyUWhT2PuxI7lgYHQW+4qG5461gNjxC1HpXbcX0By1dSZqY0B/R+Uf1LllUBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T05:57:54.712014Z"},"content_sha256":"cfb51c6b4efb571126616ee4815436af97723242faa0aab23ceb826217a13aaa","schema_version":"1.0","event_id":"sha256:cfb51c6b4efb571126616ee4815436af97723242faa0aab23ceb826217a13aaa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:M5STITKEVGKFL26IFWEVYPXHWG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Vertex distortion of lattice knots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Marion Campisi, Nicholas Cazet","submitted_at":"2020-09-08T03:38:29Z","abstract_excerpt":"The vertex distortion of a lattice knot is the supremum of the ratio of the distance between a pair of vertices along the knot and their distance in the l1-norm. We show analogous results to those of Gromov, Pardon and Blair-Campisi-Taylor-Tomova about the distortion of smooth knots hold for vertex distortion: the vertex distortion of a lattice knot is 1 only if it is the unknot, and that there are minimal lattice-stick number knot conformations with arbitrarily high distortion."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.03502","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2009.03502/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T03:43:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c6ApWEo4ou2UuKh5CvQef78yYTsI/vdWOeNQJluHdhLl4PyIHHNhs+JneqWNGselYzpPI0AWtiTX5fQZdUPCCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T05:57:54.712531Z"},"content_sha256":"4a7fc08eac97cbf49ede6dad44c77fd67404193480c432cd04cbd06ef863ddf6","schema_version":"1.0","event_id":"sha256:4a7fc08eac97cbf49ede6dad44c77fd67404193480c432cd04cbd06ef863ddf6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M5STITKEVGKFL26IFWEVYPXHWG/bundle.json","state_url":"https://pith.science/pith/M5STITKEVGKFL26IFWEVYPXHWG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M5STITKEVGKFL26IFWEVYPXHWG/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":"2026-08-15T05:57:54Z","links":{"resolver":"https://pith.science/pith/M5STITKEVGKFL26IFWEVYPXHWG","bundle":"https://pith.science/pith/M5STITKEVGKFL26IFWEVYPXHWG/bundle.json","state":"https://pith.science/pith/M5STITKEVGKFL26IFWEVYPXHWG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M5STITKEVGKFL26IFWEVYPXHWG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:M5STITKEVGKFL26IFWEVYPXHWG","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":"5e1f3bb52144821e2d9453badd2108f65dd9e852f68c8ca2a68381b3dd16dbd2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2020-09-08T03:38:29Z","title_canon_sha256":"d5a02ff5df5a694586957fa9125eda1352bd01d269e087fcf0d3ef50a10072bd"},"schema_version":"1.0","source":{"id":"2009.03502","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2009.03502","created_at":"2026-07-05T03:43:37Z"},{"alias_kind":"arxiv_version","alias_value":"2009.03502v3","created_at":"2026-07-05T03:43:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2009.03502","created_at":"2026-07-05T03:43:37Z"},{"alias_kind":"pith_short_12","alias_value":"M5STITKEVGKF","created_at":"2026-07-05T03:43:37Z"},{"alias_kind":"pith_short_16","alias_value":"M5STITKEVGKFL26I","created_at":"2026-07-05T03:43:37Z"},{"alias_kind":"pith_short_8","alias_value":"M5STITKE","created_at":"2026-07-05T03:43:37Z"}],"graph_snapshots":[{"event_id":"sha256:4a7fc08eac97cbf49ede6dad44c77fd67404193480c432cd04cbd06ef863ddf6","target":"graph","created_at":"2026-07-05T03:43:37Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2009.03502/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The vertex distortion of a lattice knot is the supremum of the ratio of the distance between a pair of vertices along the knot and their distance in the l1-norm. We show analogous results to those of Gromov, Pardon and Blair-Campisi-Taylor-Tomova about the distortion of smooth knots hold for vertex distortion: the vertex distortion of a lattice knot is 1 only if it is the unknot, and that there are minimal lattice-stick number knot conformations with arbitrarily high distortion.","authors_text":"Marion Campisi, Nicholas Cazet","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2020-09-08T03:38:29Z","title":"Vertex distortion of lattice knots"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.03502","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:cfb51c6b4efb571126616ee4815436af97723242faa0aab23ceb826217a13aaa","target":"record","created_at":"2026-07-05T03:43:37Z","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":"5e1f3bb52144821e2d9453badd2108f65dd9e852f68c8ca2a68381b3dd16dbd2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2020-09-08T03:38:29Z","title_canon_sha256":"d5a02ff5df5a694586957fa9125eda1352bd01d269e087fcf0d3ef50a10072bd"},"schema_version":"1.0","source":{"id":"2009.03502","kind":"arxiv","version":3}},"canonical_sha256":"6765344d44a99455ebc82d895c3ee7b19cb42a4bbcd49f1ab147d86abc66a76b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6765344d44a99455ebc82d895c3ee7b19cb42a4bbcd49f1ab147d86abc66a76b","first_computed_at":"2026-07-05T03:43:37.077235Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:43:37.077235Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wV6fGZ/VaafAQZ3eh7dmw2mT7y0vLVjWXo94+YHfqvD6HySYTywAWn78tglgm19FBQHWXh7/oNsF6T7TU5YGCw==","signature_status":"signed_v1","signed_at":"2026-07-05T03:43:37.077734Z","signed_message":"canonical_sha256_bytes"},"source_id":"2009.03502","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cfb51c6b4efb571126616ee4815436af97723242faa0aab23ceb826217a13aaa","sha256:4a7fc08eac97cbf49ede6dad44c77fd67404193480c432cd04cbd06ef863ddf6"],"state_sha256":"daed59525f8c41120b09271bdcf11a0f986044753a566b42ec489adfd834b8e4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Kv9AkhoVh731DCuduCEFf4vMBtxxkxW3hJtONocdM5iXzOd7HEIa3J5k5gfcHXY3zn63Lcpu8xkvG+HZawUqBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T05:57:54.716458Z","bundle_sha256":"ae3d51d46b0012adabcbfe1d8257f48aadd67d138c0560f9f6bfd1bd8f39a0bc"}}