{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:S3NXXNXQR23IJNEWS64TAA7TAO","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":"4698ffbf6b4aee744baa897e60495df89eb18dca90b2559f9fdeef99eb424f07","cross_cats_sorted":["math.CA","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-03-08T10:27:40Z","title_canon_sha256":"c6fdbc7e50ec4419d73ec5b419da4a27d62c73c327bc58af409a4262d94cd3c5"},"schema_version":"1.0","source":{"id":"1603.02464","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.02464","created_at":"2026-05-18T01:19:23Z"},{"alias_kind":"arxiv_version","alias_value":"1603.02464v1","created_at":"2026-05-18T01:19:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.02464","created_at":"2026-05-18T01:19:23Z"},{"alias_kind":"pith_short_12","alias_value":"S3NXXNXQR23I","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"S3NXXNXQR23IJNEW","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"S3NXXNXQ","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:f487848fed14a705cf7e6be6bbd62ec9fa76635e7a892f202c07daa78d453ae9","target":"graph","created_at":"2026-05-18T01:19:23Z","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":"The present chapter gives an overview on results for discrete knot energies. These discrete energies are designed to make swift numerical computations and thus open the field to computational methods. Additionally, they provide an independent, geometrically pleasing and consistent discrete model that behaves similarly to the original model. We will focus on M\\\"obius energy, integral Menger curvature and thickness.","authors_text":"Sebastian Scholtes","cross_cats":["math.CA","math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-03-08T10:27:40Z","title":"Discrete knot energies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.02464","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:c90253346d3cda105e75866c1f5910e13d9220f3de14cf7badca4c423c641dca","target":"record","created_at":"2026-05-18T01:19:23Z","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":"4698ffbf6b4aee744baa897e60495df89eb18dca90b2559f9fdeef99eb424f07","cross_cats_sorted":["math.CA","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-03-08T10:27:40Z","title_canon_sha256":"c6fdbc7e50ec4419d73ec5b419da4a27d62c73c327bc58af409a4262d94cd3c5"},"schema_version":"1.0","source":{"id":"1603.02464","kind":"arxiv","version":1}},"canonical_sha256":"96db7bb6f08eb684b49697b93003f303b288dac505518e01ce63cd01771c9001","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"96db7bb6f08eb684b49697b93003f303b288dac505518e01ce63cd01771c9001","first_computed_at":"2026-05-18T01:19:23.239004Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:23.239004Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M7XJn93VwLNZH9x+m285x4eBO1xGi7YyG4VlGVL1IIFiiHHAMX0vAcVVIDoL1UtRwnG/Z57Zao0OEyYJMalDDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:23.239628Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.02464","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c90253346d3cda105e75866c1f5910e13d9220f3de14cf7badca4c423c641dca","sha256:f487848fed14a705cf7e6be6bbd62ec9fa76635e7a892f202c07daa78d453ae9"],"state_sha256":"c89c98db20e92998efefacaab1e06f32ab365acc5f979415a75b5b980ee82197"}