{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:MDO2RVPRRYDDJ5POMEMENADS7M","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":"54fbd1e7e66e8447f0b9068e2b6233600eb671b242fc6d970000bb95736921a9","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2021-04-29T09:04:06Z","title_canon_sha256":"8abadae51a54cc6e98cc314eb12f37e7a55ffa5ca36e6780efbbc7d30856348e"},"schema_version":"1.0","source":{"id":"2104.14213","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2104.14213","created_at":"2026-07-05T02:36:14Z"},{"alias_kind":"arxiv_version","alias_value":"2104.14213v1","created_at":"2026-07-05T02:36:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2104.14213","created_at":"2026-07-05T02:36:14Z"},{"alias_kind":"pith_short_12","alias_value":"MDO2RVPRRYDD","created_at":"2026-07-05T02:36:14Z"},{"alias_kind":"pith_short_16","alias_value":"MDO2RVPRRYDDJ5PO","created_at":"2026-07-05T02:36:14Z"},{"alias_kind":"pith_short_8","alias_value":"MDO2RVPR","created_at":"2026-07-05T02:36:14Z"}],"graph_snapshots":[{"event_id":"sha256:5d71ea47f76ba4fea85aa611379fdca177c2e5f662c0415e70e3fe86f5f0a2dd","target":"graph","created_at":"2026-07-05T02:36:14Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2104.14213/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce the tree distance, a new distance measure on graphs. The tree distance can be computed in polynomial time with standard methods from convex optimization. It is based on the notion of fractional isomorphism, a characterization based on a natural system of linear equations whose integer solutions correspond to graph isomorphism. By results of Tinhofer (1986, 1991) and Dvo\\v{r}\\'ak (2010), two graphs G and H are fractionally isomorphic if and only if, for every tree T, the number of homomorphisms from T to G equals the corresponding number from T to H, which means that the tree dista","authors_text":"Jan B\\\"oker","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2021-04-29T09:04:06Z","title":"Graph Similarity and Homomorphism Densities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.14213","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:a89cd67f723cd81b494da9830f746128fcc5b44ccf2673bbcdc71599e3ca9a85","target":"record","created_at":"2026-07-05T02:36:14Z","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":"54fbd1e7e66e8447f0b9068e2b6233600eb671b242fc6d970000bb95736921a9","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2021-04-29T09:04:06Z","title_canon_sha256":"8abadae51a54cc6e98cc314eb12f37e7a55ffa5ca36e6780efbbc7d30856348e"},"schema_version":"1.0","source":{"id":"2104.14213","kind":"arxiv","version":1}},"canonical_sha256":"60dda8d5f18e0634f5ee6118468072fb12ce18f730882320c8e25eb87285479f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"60dda8d5f18e0634f5ee6118468072fb12ce18f730882320c8e25eb87285479f","first_computed_at":"2026-07-05T02:36:14.328388Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:36:14.328388Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YiOGCmcd+LujetAMuI67QrcNs/Kx3injZD4YKDw4zoCiGi73dF4DAPOSYprgMhiUnvkjaDYP+K1joWYC7kScCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T02:36:14.328798Z","signed_message":"canonical_sha256_bytes"},"source_id":"2104.14213","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a89cd67f723cd81b494da9830f746128fcc5b44ccf2673bbcdc71599e3ca9a85","sha256:5d71ea47f76ba4fea85aa611379fdca177c2e5f662c0415e70e3fe86f5f0a2dd"],"state_sha256":"b12420b3859d0dd63249ca69a9550965c47671171064fa6f3a6175cea7ba7d52"}