{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:NJQMPOSRNMBIXZD5XNYLPNEMBZ","short_pith_number":"pith:NJQMPOSR","canonical_record":{"source":{"id":"1711.00788","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2017-11-02T15:49:59Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"5d1bd55b9ff4d08c6b3d7c248a132481305ad72fdd035b1f2d4ca564b51f83ba","abstract_canon_sha256":"505ee0232f461c4d44c7215501a4c80d90f915ede841918331f5f01fadf0bd65"},"schema_version":"1.0"},"canonical_sha256":"6a60c7ba516b028be47dbb70b7b48c0e536439335ebaad00cbcd518c37f97454","source":{"kind":"arxiv","id":"1711.00788","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.00788","created_at":"2026-05-18T00:31:29Z"},{"alias_kind":"arxiv_version","alias_value":"1711.00788v1","created_at":"2026-05-18T00:31:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.00788","created_at":"2026-05-18T00:31:29Z"},{"alias_kind":"pith_short_12","alias_value":"NJQMPOSRNMBI","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"NJQMPOSRNMBIXZD5","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"NJQMPOSR","created_at":"2026-05-18T12:31:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:NJQMPOSRNMBIXZD5XNYLPNEMBZ","target":"record","payload":{"canonical_record":{"source":{"id":"1711.00788","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2017-11-02T15:49:59Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"5d1bd55b9ff4d08c6b3d7c248a132481305ad72fdd035b1f2d4ca564b51f83ba","abstract_canon_sha256":"505ee0232f461c4d44c7215501a4c80d90f915ede841918331f5f01fadf0bd65"},"schema_version":"1.0"},"canonical_sha256":"6a60c7ba516b028be47dbb70b7b48c0e536439335ebaad00cbcd518c37f97454","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:29.539366Z","signature_b64":"ogA/+l99ex1W7hL9zPoGdOJpSA3Cb4U2ZXPvk/XVEANd/aYlyxijKdBFUK2k1mW0P0reX1bniT5mWTvcoA8JDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a60c7ba516b028be47dbb70b7b48c0e536439335ebaad00cbcd518c37f97454","last_reissued_at":"2026-05-18T00:31:29.538623Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:29.538623Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.00788","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":"2026-05-18T00:31:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jnDf+5EwVouOPMeZhwxoQM967Zu2arHWo4Hr+6zFWKCJ62wFTjJkQe8vRKs8HSRmkyiiqx/bxlfuGz8sG/anAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T16:31:23.630847Z"},"content_sha256":"21e9693389cbef34230796f469127f0824c4e48b827e34cf176735617e383692","schema_version":"1.0","event_id":"sha256:21e9693389cbef34230796f469127f0824c4e48b827e34cf176735617e383692"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:NJQMPOSRNMBIXZD5XNYLPNEMBZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the complexity of optimal homotopies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CG","authors_text":"Arnaud de Mesmay, Erin Wolf Chambers, Tim Ophelders","submitted_at":"2017-11-02T15:49:59Z","abstract_excerpt":"In this article, we provide new structural results and algorithms for the Homotopy Height problem. In broad terms, this problem quantifies how much a curve on a surface needs to be stretched to sweep continuously between two positions. More precisely, given two homotopic curves $\\gamma_1$ and $\\gamma_2$ on a combinatorial (say, triangulated) surface, we investigate the problem of computing a homotopy between $\\gamma_1$ and $\\gamma_2$ where the length of the longest intermediate curve is minimized. Such optimal homotopies are relevant for a wide range of purposes, from very theoretical question"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.00788","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":"2026-05-18T00:31:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2OtRoskvBCosN3arO5dvBebQuFVY/P0wFfRhvZ6ZvZp0y0F/Ebdb716ZCdSPimf7csJM2Pc/8s0VPXNL5x4DCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T16:31:23.631272Z"},"content_sha256":"03911356ec308a23dab076b72b3f4e414fde61e5174adf59cc835a32e77b12eb","schema_version":"1.0","event_id":"sha256:03911356ec308a23dab076b72b3f4e414fde61e5174adf59cc835a32e77b12eb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NJQMPOSRNMBIXZD5XNYLPNEMBZ/bundle.json","state_url":"https://pith.science/pith/NJQMPOSRNMBIXZD5XNYLPNEMBZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NJQMPOSRNMBIXZD5XNYLPNEMBZ/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":"2026-05-30T16:31:23Z","links":{"resolver":"https://pith.science/pith/NJQMPOSRNMBIXZD5XNYLPNEMBZ","bundle":"https://pith.science/pith/NJQMPOSRNMBIXZD5XNYLPNEMBZ/bundle.json","state":"https://pith.science/pith/NJQMPOSRNMBIXZD5XNYLPNEMBZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NJQMPOSRNMBIXZD5XNYLPNEMBZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:NJQMPOSRNMBIXZD5XNYLPNEMBZ","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":"505ee0232f461c4d44c7215501a4c80d90f915ede841918331f5f01fadf0bd65","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2017-11-02T15:49:59Z","title_canon_sha256":"5d1bd55b9ff4d08c6b3d7c248a132481305ad72fdd035b1f2d4ca564b51f83ba"},"schema_version":"1.0","source":{"id":"1711.00788","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.00788","created_at":"2026-05-18T00:31:29Z"},{"alias_kind":"arxiv_version","alias_value":"1711.00788v1","created_at":"2026-05-18T00:31:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.00788","created_at":"2026-05-18T00:31:29Z"},{"alias_kind":"pith_short_12","alias_value":"NJQMPOSRNMBI","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"NJQMPOSRNMBIXZD5","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"NJQMPOSR","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:03911356ec308a23dab076b72b3f4e414fde61e5174adf59cc835a32e77b12eb","target":"graph","created_at":"2026-05-18T00:31:29Z","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":"In this article, we provide new structural results and algorithms for the Homotopy Height problem. In broad terms, this problem quantifies how much a curve on a surface needs to be stretched to sweep continuously between two positions. More precisely, given two homotopic curves $\\gamma_1$ and $\\gamma_2$ on a combinatorial (say, triangulated) surface, we investigate the problem of computing a homotopy between $\\gamma_1$ and $\\gamma_2$ where the length of the longest intermediate curve is minimized. Such optimal homotopies are relevant for a wide range of purposes, from very theoretical question","authors_text":"Arnaud de Mesmay, Erin Wolf Chambers, Tim Ophelders","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2017-11-02T15:49:59Z","title":"On the complexity of optimal homotopies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.00788","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":"sha256:21e9693389cbef34230796f469127f0824c4e48b827e34cf176735617e383692","target":"record","created_at":"2026-05-18T00:31:29Z","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":"505ee0232f461c4d44c7215501a4c80d90f915ede841918331f5f01fadf0bd65","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2017-11-02T15:49:59Z","title_canon_sha256":"5d1bd55b9ff4d08c6b3d7c248a132481305ad72fdd035b1f2d4ca564b51f83ba"},"schema_version":"1.0","source":{"id":"1711.00788","kind":"arxiv","version":1}},"canonical_sha256":"6a60c7ba516b028be47dbb70b7b48c0e536439335ebaad00cbcd518c37f97454","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a60c7ba516b028be47dbb70b7b48c0e536439335ebaad00cbcd518c37f97454","first_computed_at":"2026-05-18T00:31:29.538623Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:29.538623Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ogA/+l99ex1W7hL9zPoGdOJpSA3Cb4U2ZXPvk/XVEANd/aYlyxijKdBFUK2k1mW0P0reX1bniT5mWTvcoA8JDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:29.539366Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.00788","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:21e9693389cbef34230796f469127f0824c4e48b827e34cf176735617e383692","sha256:03911356ec308a23dab076b72b3f4e414fde61e5174adf59cc835a32e77b12eb"],"state_sha256":"daed1110f1a05289778a2d071c805cfd5d3737e6697a4bfb6682a3465c0cecea"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IfUQ9Ry6UngUmGIVOuKff2ykA7AyEs/kyFhBEauVC022AxHC4bNSZjzBkY9p5By5MsV0Nav9JGD+q/0vS4iFCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T16:31:23.634873Z","bundle_sha256":"b6891b9d3bb3ffbbf26e0f470a384fd438d9e34c292139307c9cdc3cb28c5641"}}