{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:T3CYURRBNKXYCUI3MSQHNV5KUZ","short_pith_number":"pith:T3CYURRB","canonical_record":{"source":{"id":"1303.1831","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-03-07T21:22:39Z","cross_cats_sorted":[],"title_canon_sha256":"684a75b12a9a49b59ad7c5e8bc1cfc9ce02b68fde5ccba88e37cf9907c228d42","abstract_canon_sha256":"32f51c1d6d086a80a0e4bcb8473829bb1f892ac81e3d5f5fc05b9decfa8f9b51"},"schema_version":"1.0"},"canonical_sha256":"9ec58a46216aaf81511b64a076d7aaa644e4a5aa6550deaae211c3be83ac8ada","source":{"kind":"arxiv","id":"1303.1831","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.1831","created_at":"2026-05-18T02:47:23Z"},{"alias_kind":"arxiv_version","alias_value":"1303.1831v2","created_at":"2026-05-18T02:47:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.1831","created_at":"2026-05-18T02:47:23Z"},{"alias_kind":"pith_short_12","alias_value":"T3CYURRBNKXY","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"T3CYURRBNKXYCUI3","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"T3CYURRB","created_at":"2026-05-18T12:27:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:T3CYURRBNKXYCUI3MSQHNV5KUZ","target":"record","payload":{"canonical_record":{"source":{"id":"1303.1831","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-03-07T21:22:39Z","cross_cats_sorted":[],"title_canon_sha256":"684a75b12a9a49b59ad7c5e8bc1cfc9ce02b68fde5ccba88e37cf9907c228d42","abstract_canon_sha256":"32f51c1d6d086a80a0e4bcb8473829bb1f892ac81e3d5f5fc05b9decfa8f9b51"},"schema_version":"1.0"},"canonical_sha256":"9ec58a46216aaf81511b64a076d7aaa644e4a5aa6550deaae211c3be83ac8ada","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:23.234577Z","signature_b64":"dGt7TvfFo3Wnjc1rfAFPsMpy/9rHFWzShwbQkGfL9tlYBol4fSLbyaKT4stWIzktJK6fe/ezHxIMz6ZxlZhsDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9ec58a46216aaf81511b64a076d7aaa644e4a5aa6550deaae211c3be83ac8ada","last_reissued_at":"2026-05-18T02:47:23.234187Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:23.234187Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1303.1831","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:47:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jVc0NUlrlYX94yXOhI72aJLWlVfHwh/CwEanGEeVo7DEJ6zDliixactRdOcgDFp5DlPsIYJElyTMJXmoRrAcCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T16:51:25.685753Z"},"content_sha256":"47570e42ad4d20a159160a9d4e2947b5f4388845b4f0ad901cc345c03771e8a9","schema_version":"1.0","event_id":"sha256:47570e42ad4d20a159160a9d4e2947b5f4388845b4f0ad901cc345c03771e8a9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:T3CYURRBNKXYCUI3MSQHNV5KUZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Grid Movies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Matthew Graham","submitted_at":"2013-03-07T21:22:39Z","abstract_excerpt":"We present a grid diagram analogue of Carter, Rieger and Saito's smooth movie theorem. Specifically, we give definitions for grid movies, grid movie isotopies and present a definition of grid planar isotopy as a particular subset of the grid diagram moves: stabilization, destabilization and commutation. We show that grid planar isotopy classes are in 1-1 correspondence with smooth planar isotopy classes by using a new planar grid algorithm that takes a smooth knot diagram to a grid diagram. We then present generalizations of both the smooth and grid movie theorems that apply to surfaces with b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.1831","kind":"arxiv","version":2},"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":"2026-05-18T02:47:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yRUYCeIOOEgxh3I9+UXIRMW4IgdwIqrUqQA0Uu68JLnOOAX+zrJOf+AII6WeyCMBohhliyf8HVtgFTMKYi0HDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T16:51:25.686084Z"},"content_sha256":"9459cd534ec885e11937a8365a1f33bb3f11f53bf4b1151a6ee555e4b1ee924d","schema_version":"1.0","event_id":"sha256:9459cd534ec885e11937a8365a1f33bb3f11f53bf4b1151a6ee555e4b1ee924d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T3CYURRBNKXYCUI3MSQHNV5KUZ/bundle.json","state_url":"https://pith.science/pith/T3CYURRBNKXYCUI3MSQHNV5KUZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T3CYURRBNKXYCUI3MSQHNV5KUZ/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":"2026-06-27T16:51:25Z","links":{"resolver":"https://pith.science/pith/T3CYURRBNKXYCUI3MSQHNV5KUZ","bundle":"https://pith.science/pith/T3CYURRBNKXYCUI3MSQHNV5KUZ/bundle.json","state":"https://pith.science/pith/T3CYURRBNKXYCUI3MSQHNV5KUZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T3CYURRBNKXYCUI3MSQHNV5KUZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:T3CYURRBNKXYCUI3MSQHNV5KUZ","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":"32f51c1d6d086a80a0e4bcb8473829bb1f892ac81e3d5f5fc05b9decfa8f9b51","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-03-07T21:22:39Z","title_canon_sha256":"684a75b12a9a49b59ad7c5e8bc1cfc9ce02b68fde5ccba88e37cf9907c228d42"},"schema_version":"1.0","source":{"id":"1303.1831","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.1831","created_at":"2026-05-18T02:47:23Z"},{"alias_kind":"arxiv_version","alias_value":"1303.1831v2","created_at":"2026-05-18T02:47:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.1831","created_at":"2026-05-18T02:47:23Z"},{"alias_kind":"pith_short_12","alias_value":"T3CYURRBNKXY","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"T3CYURRBNKXYCUI3","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"T3CYURRB","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:9459cd534ec885e11937a8365a1f33bb3f11f53bf4b1151a6ee555e4b1ee924d","target":"graph","created_at":"2026-05-18T02:47:23Z","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 present a grid diagram analogue of Carter, Rieger and Saito's smooth movie theorem. Specifically, we give definitions for grid movies, grid movie isotopies and present a definition of grid planar isotopy as a particular subset of the grid diagram moves: stabilization, destabilization and commutation. We show that grid planar isotopy classes are in 1-1 correspondence with smooth planar isotopy classes by using a new planar grid algorithm that takes a smooth knot diagram to a grid diagram. We then present generalizations of both the smooth and grid movie theorems that apply to surfaces with b","authors_text":"Matthew Graham","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-03-07T21:22:39Z","title":"Grid Movies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.1831","kind":"arxiv","version":2},"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":"sha256:47570e42ad4d20a159160a9d4e2947b5f4388845b4f0ad901cc345c03771e8a9","target":"record","created_at":"2026-05-18T02:47:23Z","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":"32f51c1d6d086a80a0e4bcb8473829bb1f892ac81e3d5f5fc05b9decfa8f9b51","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-03-07T21:22:39Z","title_canon_sha256":"684a75b12a9a49b59ad7c5e8bc1cfc9ce02b68fde5ccba88e37cf9907c228d42"},"schema_version":"1.0","source":{"id":"1303.1831","kind":"arxiv","version":2}},"canonical_sha256":"9ec58a46216aaf81511b64a076d7aaa644e4a5aa6550deaae211c3be83ac8ada","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9ec58a46216aaf81511b64a076d7aaa644e4a5aa6550deaae211c3be83ac8ada","first_computed_at":"2026-05-18T02:47:23.234187Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:47:23.234187Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dGt7TvfFo3Wnjc1rfAFPsMpy/9rHFWzShwbQkGfL9tlYBol4fSLbyaKT4stWIzktJK6fe/ezHxIMz6ZxlZhsDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:47:23.234577Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.1831","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47570e42ad4d20a159160a9d4e2947b5f4388845b4f0ad901cc345c03771e8a9","sha256:9459cd534ec885e11937a8365a1f33bb3f11f53bf4b1151a6ee555e4b1ee924d"],"state_sha256":"8277c4b002dfe12fb0eb890cc6b2c8afcd2897947a1a7c932a093fbb614d03f8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1BrYRSledBAuPU6XgBEa2OKnqHz7qLTjXctMBxNK1CIZG49qeRN1Dybc4ZUfg35C1BQxNwcjeGwDtSnfxbXJCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T16:51:25.687907Z","bundle_sha256":"39244759ff6215fbc07b58bd32167578b12142117e2af783e936cddef4dead69"}}