{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:ANEEEPXHG4WJ62YMS5M4PKTSUF","short_pith_number":"pith:ANEEEPXH","canonical_record":{"source":{"id":"2407.02102","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-07-02T09:40:20Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"4752db4b6d452da0b370b0a8615adf0175c3bbd27b0230ecaf27da9773955524","abstract_canon_sha256":"125988d3830e1a8f6763657c517a5d2c65be07fdfe220bb57385a0ca2120e8d7"},"schema_version":"1.0"},"canonical_sha256":"0348423ee7372c9f6b0c9759c7aa72a161ab9f5021e37663b1cc91ff45af3dde","source":{"kind":"arxiv","id":"2407.02102","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.02102","created_at":"2026-07-05T08:39:10Z"},{"alias_kind":"arxiv_version","alias_value":"2407.02102v1","created_at":"2026-07-05T08:39:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.02102","created_at":"2026-07-05T08:39:10Z"},{"alias_kind":"pith_short_12","alias_value":"ANEEEPXHG4WJ","created_at":"2026-07-05T08:39:10Z"},{"alias_kind":"pith_short_16","alias_value":"ANEEEPXHG4WJ62YM","created_at":"2026-07-05T08:39:10Z"},{"alias_kind":"pith_short_8","alias_value":"ANEEEPXH","created_at":"2026-07-05T08:39:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:ANEEEPXHG4WJ62YMS5M4PKTSUF","target":"record","payload":{"canonical_record":{"source":{"id":"2407.02102","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-07-02T09:40:20Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"4752db4b6d452da0b370b0a8615adf0175c3bbd27b0230ecaf27da9773955524","abstract_canon_sha256":"125988d3830e1a8f6763657c517a5d2c65be07fdfe220bb57385a0ca2120e8d7"},"schema_version":"1.0"},"canonical_sha256":"0348423ee7372c9f6b0c9759c7aa72a161ab9f5021e37663b1cc91ff45af3dde","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:39:10.113457Z","signature_b64":"YR3u4p2+LJTGuXWT1/07PzkrQxPpqsLXf79rn5a7h/scLyYpiPyrHFIIb7RgwzIViOFUvNtQ870VTxG060yiDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0348423ee7372c9f6b0c9759c7aa72a161ab9f5021e37663b1cc91ff45af3dde","last_reissued_at":"2026-07-05T08:39:10.112959Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:39:10.112959Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2407.02102","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":"2026-07-05T08:39:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"saOsaNnEYaMGQUhYTa7Zm7W/QX4XkEdHAdcief1A19drc1DLkDcPNtLE7iXFz2XSy4zjqcCFLeLvCY+VkBakBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T18:23:38.106394Z"},"content_sha256":"23ebd5d2a00f75af8589eadc652a6bf645b361d4d8d430c62daa1c7aae5e6571","schema_version":"1.0","event_id":"sha256:23ebd5d2a00f75af8589eadc652a6bf645b361d4d8d430c62daa1c7aae5e6571"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:ANEEEPXHG4WJ62YMS5M4PKTSUF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Separating the edges of a graph by cycles and by subdivisions of $K_4$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"F\\'abio Botler, T\\'assio Naia","submitted_at":"2024-07-02T09:40:20Z","abstract_excerpt":"A separating system of a graph $G$ is a family $\\mathcal{S}$ of subgraphs of $G$ for which the following holds: for all distinct edges $e$ and $f$ of $G$, there exists an element in $\\mathcal{S}$ that contains $e$ but not $f$. Recently, it has been shown that every graph of order $n$ admits a separating system consisting of $19n$ paths [Bonamy, Botler, Dross, Naia, Skokan, Separating the Edges of a Graph by a Linear Number of Paths, Adv. Comb., October 2023], improving the previous almost linear bound of $\\mathrm{O}(n\\log^\\star n)$ [S. Letzter, Separating paths systems of almost linear size, T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.02102","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2407.02102/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T08:39:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ve+NIeOztwdoa+i2TKJeHiVCZbWtlvbRVpctgBsXiCzq2HYiR0MousWJr6uZ7U/PpMlavypxS0yigcLGessFBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T18:23:38.107336Z"},"content_sha256":"437ed7f70f9a6a809af319967a193c334fdb428b9e9b83f4ea55a688ca4031ea","schema_version":"1.0","event_id":"sha256:437ed7f70f9a6a809af319967a193c334fdb428b9e9b83f4ea55a688ca4031ea"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ANEEEPXHG4WJ62YMS5M4PKTSUF/bundle.json","state_url":"https://pith.science/pith/ANEEEPXHG4WJ62YMS5M4PKTSUF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ANEEEPXHG4WJ62YMS5M4PKTSUF/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":"2026-08-13T18:23:38Z","links":{"resolver":"https://pith.science/pith/ANEEEPXHG4WJ62YMS5M4PKTSUF","bundle":"https://pith.science/pith/ANEEEPXHG4WJ62YMS5M4PKTSUF/bundle.json","state":"https://pith.science/pith/ANEEEPXHG4WJ62YMS5M4PKTSUF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ANEEEPXHG4WJ62YMS5M4PKTSUF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:ANEEEPXHG4WJ62YMS5M4PKTSUF","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":"125988d3830e1a8f6763657c517a5d2c65be07fdfe220bb57385a0ca2120e8d7","cross_cats_sorted":["cs.DM"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-07-02T09:40:20Z","title_canon_sha256":"4752db4b6d452da0b370b0a8615adf0175c3bbd27b0230ecaf27da9773955524"},"schema_version":"1.0","source":{"id":"2407.02102","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.02102","created_at":"2026-07-05T08:39:10Z"},{"alias_kind":"arxiv_version","alias_value":"2407.02102v1","created_at":"2026-07-05T08:39:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.02102","created_at":"2026-07-05T08:39:10Z"},{"alias_kind":"pith_short_12","alias_value":"ANEEEPXHG4WJ","created_at":"2026-07-05T08:39:10Z"},{"alias_kind":"pith_short_16","alias_value":"ANEEEPXHG4WJ62YM","created_at":"2026-07-05T08:39:10Z"},{"alias_kind":"pith_short_8","alias_value":"ANEEEPXH","created_at":"2026-07-05T08:39:10Z"}],"graph_snapshots":[{"event_id":"sha256:437ed7f70f9a6a809af319967a193c334fdb428b9e9b83f4ea55a688ca4031ea","target":"graph","created_at":"2026-07-05T08:39:10Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2407.02102/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A separating system of a graph $G$ is a family $\\mathcal{S}$ of subgraphs of $G$ for which the following holds: for all distinct edges $e$ and $f$ of $G$, there exists an element in $\\mathcal{S}$ that contains $e$ but not $f$. Recently, it has been shown that every graph of order $n$ admits a separating system consisting of $19n$ paths [Bonamy, Botler, Dross, Naia, Skokan, Separating the Edges of a Graph by a Linear Number of Paths, Adv. Comb., October 2023], improving the previous almost linear bound of $\\mathrm{O}(n\\log^\\star n)$ [S. Letzter, Separating paths systems of almost linear size, T","authors_text":"F\\'abio Botler, T\\'assio Naia","cross_cats":["cs.DM"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-07-02T09:40:20Z","title":"Separating the edges of a graph by cycles and by subdivisions of $K_4$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.02102","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":"sha256:23ebd5d2a00f75af8589eadc652a6bf645b361d4d8d430c62daa1c7aae5e6571","target":"record","created_at":"2026-07-05T08:39:10Z","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":"125988d3830e1a8f6763657c517a5d2c65be07fdfe220bb57385a0ca2120e8d7","cross_cats_sorted":["cs.DM"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-07-02T09:40:20Z","title_canon_sha256":"4752db4b6d452da0b370b0a8615adf0175c3bbd27b0230ecaf27da9773955524"},"schema_version":"1.0","source":{"id":"2407.02102","kind":"arxiv","version":1}},"canonical_sha256":"0348423ee7372c9f6b0c9759c7aa72a161ab9f5021e37663b1cc91ff45af3dde","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0348423ee7372c9f6b0c9759c7aa72a161ab9f5021e37663b1cc91ff45af3dde","first_computed_at":"2026-07-05T08:39:10.112959Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:39:10.112959Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YR3u4p2+LJTGuXWT1/07PzkrQxPpqsLXf79rn5a7h/scLyYpiPyrHFIIb7RgwzIViOFUvNtQ870VTxG060yiDg==","signature_status":"signed_v1","signed_at":"2026-07-05T08:39:10.113457Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.02102","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:23ebd5d2a00f75af8589eadc652a6bf645b361d4d8d430c62daa1c7aae5e6571","sha256:437ed7f70f9a6a809af319967a193c334fdb428b9e9b83f4ea55a688ca4031ea"],"state_sha256":"a0fb6ba255b6e02848c4f26d75b6f1c34ffa15878da288a1f06376376f859b98"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Yl/rhJYlohsBNmqYMuKSLyewcJbeUVdKwfXSPD1MqU20re6qkeCeM6l+Y2Ga6DJhX7ndCsH+NLRzfrEN9T6PCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T18:23:38.113864Z","bundle_sha256":"5e63223f3d3a3d23d22c59fe3f6ba58b2ce71d719fb976c84e07b8cf939b5596"}}