{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:OFKOZLFOD2A36X4GBK6DETUXAY","short_pith_number":"pith:OFKOZLFO","canonical_record":{"source":{"id":"2406.02514","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-06-04T17:37:13Z","cross_cats_sorted":[],"title_canon_sha256":"adfe72d3125e1d94868632794fa2a80c8c0d34415e707b4e6931cd53fed77a6b","abstract_canon_sha256":"0bc9ca79000e46a1534036bed35ab72521e442487d80f228f922a797e6bb0702"},"schema_version":"1.0"},"canonical_sha256":"7154ecacae1e81bf5f860abc324e9706331f38952753e8dead7f0074851999b8","source":{"kind":"arxiv","id":"2406.02514","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.02514","created_at":"2026-07-05T08:27:20Z"},{"alias_kind":"arxiv_version","alias_value":"2406.02514v1","created_at":"2026-07-05T08:27:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.02514","created_at":"2026-07-05T08:27:20Z"},{"alias_kind":"pith_short_12","alias_value":"OFKOZLFOD2A3","created_at":"2026-07-05T08:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"OFKOZLFOD2A36X4G","created_at":"2026-07-05T08:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"OFKOZLFO","created_at":"2026-07-05T08:27:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:OFKOZLFOD2A36X4GBK6DETUXAY","target":"record","payload":{"canonical_record":{"source":{"id":"2406.02514","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-06-04T17:37:13Z","cross_cats_sorted":[],"title_canon_sha256":"adfe72d3125e1d94868632794fa2a80c8c0d34415e707b4e6931cd53fed77a6b","abstract_canon_sha256":"0bc9ca79000e46a1534036bed35ab72521e442487d80f228f922a797e6bb0702"},"schema_version":"1.0"},"canonical_sha256":"7154ecacae1e81bf5f860abc324e9706331f38952753e8dead7f0074851999b8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:27:20.825254Z","signature_b64":"Ktnc5n6r+P9PfGEyDcV+tUer+aNB5uYnwi9ZZF/rLEG//Wyqr7f4XVkrrR8QY4B+hwiQlRx3HKv2n+sNK4qkCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7154ecacae1e81bf5f860abc324e9706331f38952753e8dead7f0074851999b8","last_reissued_at":"2026-07-05T08:27:20.824818Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:27:20.824818Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2406.02514","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":"2026-07-05T08:27:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V+gPEhES3RN6/L28bk8fT/sHjvUMfgT+Qt0J9ZKOVqID2qgIGnfk5vZt8qhiR89wscx+N8rAiWf229ZxXQ14AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T07:25:35.085503Z"},"content_sha256":"c58e2f93de30b1769da7cf6c1b60c41dab5fde969129848ac9e22aa0744384a5","schema_version":"1.0","event_id":"sha256:c58e2f93de30b1769da7cf6c1b60c41dab5fde969129848ac9e22aa0744384a5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:OFKOZLFOD2A36X4GBK6DETUXAY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Approximate path decompositions of regular graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alexey Pokrovskiy, Alp M\\\"uyesser, Benny Sudakov, Richard Montgomery","submitted_at":"2024-06-04T17:37:13Z","abstract_excerpt":"We show that the edges of any $d$-regular graph can be almost decomposed into paths of length roughly $d$, giving an approximate solution to a problem of Kotzig from 1957. Along the way, we show that almost all of the vertices of a $d$-regular graph can be partitioned into $n/(d+1)$ paths, asymptotically confirming a conjecture of Magnant and Martin from 2009."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.02514","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/2406.02514/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":"2026-07-05T08:27:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FSJX84oha/xTpG2F9g+2aU/+xUxdpJONEbV6o066mjgvCE6BV6NrsA+Aq9P1NoKYXb+T3vozzw6zr5oynywRAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T07:25:35.086018Z"},"content_sha256":"d60a2b0a6a976b42970d2f30b0341b7275f24d138a8f751040658666baf50285","schema_version":"1.0","event_id":"sha256:d60a2b0a6a976b42970d2f30b0341b7275f24d138a8f751040658666baf50285"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OFKOZLFOD2A36X4GBK6DETUXAY/bundle.json","state_url":"https://pith.science/pith/OFKOZLFOD2A36X4GBK6DETUXAY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OFKOZLFOD2A36X4GBK6DETUXAY/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":"2026-08-09T07:25:35Z","links":{"resolver":"https://pith.science/pith/OFKOZLFOD2A36X4GBK6DETUXAY","bundle":"https://pith.science/pith/OFKOZLFOD2A36X4GBK6DETUXAY/bundle.json","state":"https://pith.science/pith/OFKOZLFOD2A36X4GBK6DETUXAY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OFKOZLFOD2A36X4GBK6DETUXAY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:OFKOZLFOD2A36X4GBK6DETUXAY","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":"0bc9ca79000e46a1534036bed35ab72521e442487d80f228f922a797e6bb0702","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-06-04T17:37:13Z","title_canon_sha256":"adfe72d3125e1d94868632794fa2a80c8c0d34415e707b4e6931cd53fed77a6b"},"schema_version":"1.0","source":{"id":"2406.02514","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.02514","created_at":"2026-07-05T08:27:20Z"},{"alias_kind":"arxiv_version","alias_value":"2406.02514v1","created_at":"2026-07-05T08:27:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.02514","created_at":"2026-07-05T08:27:20Z"},{"alias_kind":"pith_short_12","alias_value":"OFKOZLFOD2A3","created_at":"2026-07-05T08:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"OFKOZLFOD2A36X4G","created_at":"2026-07-05T08:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"OFKOZLFO","created_at":"2026-07-05T08:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:d60a2b0a6a976b42970d2f30b0341b7275f24d138a8f751040658666baf50285","target":"graph","created_at":"2026-07-05T08:27:20Z","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/2406.02514/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that the edges of any $d$-regular graph can be almost decomposed into paths of length roughly $d$, giving an approximate solution to a problem of Kotzig from 1957. Along the way, we show that almost all of the vertices of a $d$-regular graph can be partitioned into $n/(d+1)$ paths, asymptotically confirming a conjecture of Magnant and Martin from 2009.","authors_text":"Alexey Pokrovskiy, Alp M\\\"uyesser, Benny Sudakov, Richard Montgomery","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-06-04T17:37:13Z","title":"Approximate path decompositions of regular graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.02514","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:c58e2f93de30b1769da7cf6c1b60c41dab5fde969129848ac9e22aa0744384a5","target":"record","created_at":"2026-07-05T08:27:20Z","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":"0bc9ca79000e46a1534036bed35ab72521e442487d80f228f922a797e6bb0702","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-06-04T17:37:13Z","title_canon_sha256":"adfe72d3125e1d94868632794fa2a80c8c0d34415e707b4e6931cd53fed77a6b"},"schema_version":"1.0","source":{"id":"2406.02514","kind":"arxiv","version":1}},"canonical_sha256":"7154ecacae1e81bf5f860abc324e9706331f38952753e8dead7f0074851999b8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7154ecacae1e81bf5f860abc324e9706331f38952753e8dead7f0074851999b8","first_computed_at":"2026-07-05T08:27:20.824818Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:27:20.824818Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ktnc5n6r+P9PfGEyDcV+tUer+aNB5uYnwi9ZZF/rLEG//Wyqr7f4XVkrrR8QY4B+hwiQlRx3HKv2n+sNK4qkCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:27:20.825254Z","signed_message":"canonical_sha256_bytes"},"source_id":"2406.02514","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c58e2f93de30b1769da7cf6c1b60c41dab5fde969129848ac9e22aa0744384a5","sha256:d60a2b0a6a976b42970d2f30b0341b7275f24d138a8f751040658666baf50285"],"state_sha256":"426d5bbe9cf8ec0efd7bf8d4bfb54568f29a75446cd5bb90332c9ffeee9569ac"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XdfGA4WSLlbptrqqEMVHbqtu4pEj+KgiQk80DuQqx/5ada/rEIdX/ZodPaLkUPcM1MOur3xmsgNUl1sAAOjBDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T07:25:35.089809Z","bundle_sha256":"3831fe5c50e13dc543bcd18ea289e118388a4745f77be8e2ff8fcc24980edf88"}}