{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:5YEIWKNDF4ZAK6OFBT3CB7CHDP","short_pith_number":"pith:5YEIWKND","canonical_record":{"source":{"id":"1609.01266","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2016-09-05T19:44:02Z","cross_cats_sorted":[],"title_canon_sha256":"8180765487f0578803db14b578916ae0e547108453b35b7323885f355a65f609","abstract_canon_sha256":"1b716c764761f4bdeab2eec2449e9370a7bac451273568b1ab7be967a26d23e5"},"schema_version":"1.0"},"canonical_sha256":"ee088b29a32f320579c50cf620fc471bc47c85b1f575917681294a344d9a5c76","source":{"kind":"arxiv","id":"1609.01266","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.01266","created_at":"2026-05-18T00:33:23Z"},{"alias_kind":"arxiv_version","alias_value":"1609.01266v3","created_at":"2026-05-18T00:33:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.01266","created_at":"2026-05-18T00:33:23Z"},{"alias_kind":"pith_short_12","alias_value":"5YEIWKNDF4ZA","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5YEIWKNDF4ZAK6OF","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5YEIWKND","created_at":"2026-05-18T12:30:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:5YEIWKNDF4ZAK6OFBT3CB7CHDP","target":"record","payload":{"canonical_record":{"source":{"id":"1609.01266","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2016-09-05T19:44:02Z","cross_cats_sorted":[],"title_canon_sha256":"8180765487f0578803db14b578916ae0e547108453b35b7323885f355a65f609","abstract_canon_sha256":"1b716c764761f4bdeab2eec2449e9370a7bac451273568b1ab7be967a26d23e5"},"schema_version":"1.0"},"canonical_sha256":"ee088b29a32f320579c50cf620fc471bc47c85b1f575917681294a344d9a5c76","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:23.086902Z","signature_b64":"zjwkYfj9d+0T1PKrWH6F5UBPVQ2PxY25uS048huI77G+MZoyjUHg/36e9ok3lRkpCTfJ1g2Q97jgxZ0hBNEmAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ee088b29a32f320579c50cf620fc471bc47c85b1f575917681294a344d9a5c76","last_reissued_at":"2026-05-18T00:33:23.086164Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:23.086164Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.01266","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":"2026-05-18T00:33:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WchWXs+OxTO9uW92dQb5kxRu0QBSMKOMnWPKN5khqawGyN9aE+F+OxUEC0TuwJgPlpPTzhMl+Ya8HkxFLvx3Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T02:19:18.841608Z"},"content_sha256":"18f1dd17bbccad18876af52567e0e1cf896a191852b506d44fcfe7aef74bce6a","schema_version":"1.0","event_id":"sha256:18f1dd17bbccad18876af52567e0e1cf896a191852b506d44fcfe7aef74bce6a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:5YEIWKNDF4ZAK6OFBT3CB7CHDP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Minimal and minimum unit circular-arc models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Francisco J. Soulignac, Pablo Terlisky","submitted_at":"2016-09-05T19:44:02Z","abstract_excerpt":"A proper circular-arc (PCA) model is a pair ${\\cal M} = (C, \\cal A)$ where $C$ is a circle and $\\cal A$ is a family of inclusion-free arcs on $C$ in which no two arcs of $\\cal A$ cover $C$. A PCA model $\\cal U = (C,\\cal A)$ is a $(c, \\ell)$-CA model when $C$ has circumference $c$, all the arcs in $\\cal A$ have length $\\ell$, and all the extremes of the arcs in $\\cal A$ are at a distance at least $1$. If $c \\leq c'$ and $\\ell \\leq \\ell'$ for every $(c', \\ell')$-CA model equivalent (resp. isomorphic) to $\\cal U$, then $\\cal U$ is minimal (resp. minimum). In this article we prove that every PCA m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.01266","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":""},"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":"2026-05-18T00:33:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u2X0/CPyU8UQZC/4SiTpnq13jrebBd6SpCn7Z9/Md9d8hLhsKfsNVGAsN0RGCAvk7YiJhak7+K4KRGZCnN/8AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T02:19:18.841956Z"},"content_sha256":"78cba3e45f60be6d82927dc7198b810b8c7d71b8ef0c4f52469b6d3d66dac9ee","schema_version":"1.0","event_id":"sha256:78cba3e45f60be6d82927dc7198b810b8c7d71b8ef0c4f52469b6d3d66dac9ee"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5YEIWKNDF4ZAK6OFBT3CB7CHDP/bundle.json","state_url":"https://pith.science/pith/5YEIWKNDF4ZAK6OFBT3CB7CHDP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5YEIWKNDF4ZAK6OFBT3CB7CHDP/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":"2026-05-28T02:19:18Z","links":{"resolver":"https://pith.science/pith/5YEIWKNDF4ZAK6OFBT3CB7CHDP","bundle":"https://pith.science/pith/5YEIWKNDF4ZAK6OFBT3CB7CHDP/bundle.json","state":"https://pith.science/pith/5YEIWKNDF4ZAK6OFBT3CB7CHDP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5YEIWKNDF4ZAK6OFBT3CB7CHDP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:5YEIWKNDF4ZAK6OFBT3CB7CHDP","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":"1b716c764761f4bdeab2eec2449e9370a7bac451273568b1ab7be967a26d23e5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2016-09-05T19:44:02Z","title_canon_sha256":"8180765487f0578803db14b578916ae0e547108453b35b7323885f355a65f609"},"schema_version":"1.0","source":{"id":"1609.01266","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.01266","created_at":"2026-05-18T00:33:23Z"},{"alias_kind":"arxiv_version","alias_value":"1609.01266v3","created_at":"2026-05-18T00:33:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.01266","created_at":"2026-05-18T00:33:23Z"},{"alias_kind":"pith_short_12","alias_value":"5YEIWKNDF4ZA","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5YEIWKNDF4ZAK6OF","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5YEIWKND","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:78cba3e45f60be6d82927dc7198b810b8c7d71b8ef0c4f52469b6d3d66dac9ee","target":"graph","created_at":"2026-05-18T00:33:23Z","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":"A proper circular-arc (PCA) model is a pair ${\\cal M} = (C, \\cal A)$ where $C$ is a circle and $\\cal A$ is a family of inclusion-free arcs on $C$ in which no two arcs of $\\cal A$ cover $C$. A PCA model $\\cal U = (C,\\cal A)$ is a $(c, \\ell)$-CA model when $C$ has circumference $c$, all the arcs in $\\cal A$ have length $\\ell$, and all the extremes of the arcs in $\\cal A$ are at a distance at least $1$. If $c \\leq c'$ and $\\ell \\leq \\ell'$ for every $(c', \\ell')$-CA model equivalent (resp. isomorphic) to $\\cal U$, then $\\cal U$ is minimal (resp. minimum). In this article we prove that every PCA m","authors_text":"Francisco J. Soulignac, Pablo Terlisky","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2016-09-05T19:44:02Z","title":"Minimal and minimum unit circular-arc models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.01266","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":"sha256:18f1dd17bbccad18876af52567e0e1cf896a191852b506d44fcfe7aef74bce6a","target":"record","created_at":"2026-05-18T00:33:23Z","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":"1b716c764761f4bdeab2eec2449e9370a7bac451273568b1ab7be967a26d23e5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2016-09-05T19:44:02Z","title_canon_sha256":"8180765487f0578803db14b578916ae0e547108453b35b7323885f355a65f609"},"schema_version":"1.0","source":{"id":"1609.01266","kind":"arxiv","version":3}},"canonical_sha256":"ee088b29a32f320579c50cf620fc471bc47c85b1f575917681294a344d9a5c76","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ee088b29a32f320579c50cf620fc471bc47c85b1f575917681294a344d9a5c76","first_computed_at":"2026-05-18T00:33:23.086164Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:23.086164Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zjwkYfj9d+0T1PKrWH6F5UBPVQ2PxY25uS048huI77G+MZoyjUHg/36e9ok3lRkpCTfJ1g2Q97jgxZ0hBNEmAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:23.086902Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.01266","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:18f1dd17bbccad18876af52567e0e1cf896a191852b506d44fcfe7aef74bce6a","sha256:78cba3e45f60be6d82927dc7198b810b8c7d71b8ef0c4f52469b6d3d66dac9ee"],"state_sha256":"26bce36360ab92685f15cb4be600f1c76f92c45fe083d084d39f03282e55a7fb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+XHW7PdVy0RwiuVaAH7MojOM1keF6JCEDHZ8qfHEgX9JAoA+77WjARDkRLsV5WahZXDqYAXx9CAMXhAGCXMiDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T02:19:18.844306Z","bundle_sha256":"b6c40e67bf0120f204082e3717109baa9ac2812c78871deac9493d4924b1d0aa"}}