{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:4FWUCX6VRJP2DP45UW5IL53VOZ","short_pith_number":"pith:4FWUCX6V","canonical_record":{"source":{"id":"1504.04616","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-04-17T19:52:27Z","cross_cats_sorted":["cs.DS","math.CO","q-bio.GN"],"title_canon_sha256":"ad6618416d239a6e206f243883748bac0fe6faeeb728dc35084550bd727388a3","abstract_canon_sha256":"26a435b00840cbe48c5f506c6c3953c58a8deb38a8a89e37c1f84ed8538db0b5"},"schema_version":"1.0"},"canonical_sha256":"e16d415fd58a5fa1bf9da5ba85f775765535f92133aaadc8e885325c429207ee","source":{"kind":"arxiv","id":"1504.04616","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.04616","created_at":"2026-05-18T02:18:14Z"},{"alias_kind":"arxiv_version","alias_value":"1504.04616v1","created_at":"2026-05-18T02:18:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.04616","created_at":"2026-05-18T02:18:14Z"},{"alias_kind":"pith_short_12","alias_value":"4FWUCX6VRJP2","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4FWUCX6VRJP2DP45","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4FWUCX6V","created_at":"2026-05-18T12:29:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:4FWUCX6VRJP2DP45UW5IL53VOZ","target":"record","payload":{"canonical_record":{"source":{"id":"1504.04616","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-04-17T19:52:27Z","cross_cats_sorted":["cs.DS","math.CO","q-bio.GN"],"title_canon_sha256":"ad6618416d239a6e206f243883748bac0fe6faeeb728dc35084550bd727388a3","abstract_canon_sha256":"26a435b00840cbe48c5f506c6c3953c58a8deb38a8a89e37c1f84ed8538db0b5"},"schema_version":"1.0"},"canonical_sha256":"e16d415fd58a5fa1bf9da5ba85f775765535f92133aaadc8e885325c429207ee","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:14.922586Z","signature_b64":"ZiEb8yecD3JdKVuBnNBKOULe23KxBYSZGfMVi4dYVP/0K+8LICgOAEV5iyDjx/aRxHXbQsydDXQQlNb9Lr18AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e16d415fd58a5fa1bf9da5ba85f775765535f92133aaadc8e885325c429207ee","last_reissued_at":"2026-05-18T02:18:14.922114Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:14.922114Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.04616","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":"2026-05-18T02:18:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i4U3qlxpTE3bRi29USj85ELazLs3AF2hMmnsuz3GThiz4ssP2qKGDSIfE/JPcD4BuL22EToJDHKnV+STB80kDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T14:32:21.471840Z"},"content_sha256":"5b50944819f2e702f7948526a55f4db7252997420b50eb0cbc1df6c41b3d4c56","schema_version":"1.0","event_id":"sha256:5b50944819f2e702f7948526a55f4db7252997420b50eb0cbc1df6c41b3d4c56"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:4FWUCX6VRJP2DP45UW5IL53VOZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the readability of overlap digraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math.CO","q-bio.GN"],"primary_cat":"cs.DM","authors_text":"Martin Milanic, Paul Medvedev, Rayan Chikhi, Sofya Raskhodnikova","submitted_at":"2015-04-17T19:52:27Z","abstract_excerpt":"We introduce the graph parameter readability and study it as a function of the number of vertices in a graph. Given a digraph D, an injective overlap labeling assigns a unique string to each vertex such that there is an arc from x to y if and only if x properly overlaps y. The readability of D is the minimum string length for which an injective overlap labeling exists. In applications that utilize overlap digraphs (e.g., in bioinformatics), readability reflects the length of the strings from which the overlap digraph is constructed. We study the asymptotic behaviour of readability by casting i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04616","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":"2026-05-18T02:18:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UoVB6CosyjZjSkrG0Sg2bRiQ14O/PwmNDmUv5M1fveilPlQ1oj9Uwb6uecj5OQFrBwmf+rikiZsjbqdPJlz0Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T14:32:21.472228Z"},"content_sha256":"bf7fdfa3784fcfa2e0b4a95d4f07084fd832c5fe7542721426d340f7b2dd7ba5","schema_version":"1.0","event_id":"sha256:bf7fdfa3784fcfa2e0b4a95d4f07084fd832c5fe7542721426d340f7b2dd7ba5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4FWUCX6VRJP2DP45UW5IL53VOZ/bundle.json","state_url":"https://pith.science/pith/4FWUCX6VRJP2DP45UW5IL53VOZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4FWUCX6VRJP2DP45UW5IL53VOZ/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":"2026-05-24T14:32:21Z","links":{"resolver":"https://pith.science/pith/4FWUCX6VRJP2DP45UW5IL53VOZ","bundle":"https://pith.science/pith/4FWUCX6VRJP2DP45UW5IL53VOZ/bundle.json","state":"https://pith.science/pith/4FWUCX6VRJP2DP45UW5IL53VOZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4FWUCX6VRJP2DP45UW5IL53VOZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:4FWUCX6VRJP2DP45UW5IL53VOZ","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":"26a435b00840cbe48c5f506c6c3953c58a8deb38a8a89e37c1f84ed8538db0b5","cross_cats_sorted":["cs.DS","math.CO","q-bio.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-04-17T19:52:27Z","title_canon_sha256":"ad6618416d239a6e206f243883748bac0fe6faeeb728dc35084550bd727388a3"},"schema_version":"1.0","source":{"id":"1504.04616","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.04616","created_at":"2026-05-18T02:18:14Z"},{"alias_kind":"arxiv_version","alias_value":"1504.04616v1","created_at":"2026-05-18T02:18:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.04616","created_at":"2026-05-18T02:18:14Z"},{"alias_kind":"pith_short_12","alias_value":"4FWUCX6VRJP2","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4FWUCX6VRJP2DP45","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4FWUCX6V","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:bf7fdfa3784fcfa2e0b4a95d4f07084fd832c5fe7542721426d340f7b2dd7ba5","target":"graph","created_at":"2026-05-18T02:18:14Z","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 introduce the graph parameter readability and study it as a function of the number of vertices in a graph. Given a digraph D, an injective overlap labeling assigns a unique string to each vertex such that there is an arc from x to y if and only if x properly overlaps y. The readability of D is the minimum string length for which an injective overlap labeling exists. In applications that utilize overlap digraphs (e.g., in bioinformatics), readability reflects the length of the strings from which the overlap digraph is constructed. We study the asymptotic behaviour of readability by casting i","authors_text":"Martin Milanic, Paul Medvedev, Rayan Chikhi, Sofya Raskhodnikova","cross_cats":["cs.DS","math.CO","q-bio.GN"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-04-17T19:52:27Z","title":"On the readability of overlap digraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04616","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":"sha256:5b50944819f2e702f7948526a55f4db7252997420b50eb0cbc1df6c41b3d4c56","target":"record","created_at":"2026-05-18T02:18:14Z","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":"26a435b00840cbe48c5f506c6c3953c58a8deb38a8a89e37c1f84ed8538db0b5","cross_cats_sorted":["cs.DS","math.CO","q-bio.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-04-17T19:52:27Z","title_canon_sha256":"ad6618416d239a6e206f243883748bac0fe6faeeb728dc35084550bd727388a3"},"schema_version":"1.0","source":{"id":"1504.04616","kind":"arxiv","version":1}},"canonical_sha256":"e16d415fd58a5fa1bf9da5ba85f775765535f92133aaadc8e885325c429207ee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e16d415fd58a5fa1bf9da5ba85f775765535f92133aaadc8e885325c429207ee","first_computed_at":"2026-05-18T02:18:14.922114Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:18:14.922114Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZiEb8yecD3JdKVuBnNBKOULe23KxBYSZGfMVi4dYVP/0K+8LICgOAEV5iyDjx/aRxHXbQsydDXQQlNb9Lr18AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:18:14.922586Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.04616","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5b50944819f2e702f7948526a55f4db7252997420b50eb0cbc1df6c41b3d4c56","sha256:bf7fdfa3784fcfa2e0b4a95d4f07084fd832c5fe7542721426d340f7b2dd7ba5"],"state_sha256":"98119a1c4be0f5e817ae2ee5cfece6248b0e3fb8ddbe5139626abf8ed233e7df"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s4LXLc9tAkx1d3gNsH03y3zVqsi7A/mgW0s3gsBOYmYiLW2HQ39lYvsKpTeZavAajqHXt8cIpUwg5XSWbmO4Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T14:32:21.475815Z","bundle_sha256":"967b71edfeaa1d7f109fcc6038869aadd403b12c1e66941271764553392d3dbf"}}