{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:Y5PYV4HAKCON5I22IRBB2LR3I4","short_pith_number":"pith:Y5PYV4HA","canonical_record":{"source":{"id":"1410.2164","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-08T15:28:09Z","cross_cats_sorted":[],"title_canon_sha256":"5664562ac9b5cca8b57fae17488cb0880aa38a464cae68cee2fb4d33c025e05f","abstract_canon_sha256":"8ba506c0c6084b49d7b1fcbc69de1ade948dcc75c6e086809a9ede5e21cbc2bb"},"schema_version":"1.0"},"canonical_sha256":"c75f8af0e0509cdea35a44421d2e3b4719c15e45f2ccc81eb76b8d0abe6def29","source":{"kind":"arxiv","id":"1410.2164","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.2164","created_at":"2026-05-18T02:39:39Z"},{"alias_kind":"arxiv_version","alias_value":"1410.2164v3","created_at":"2026-05-18T02:39:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.2164","created_at":"2026-05-18T02:39:39Z"},{"alias_kind":"pith_short_12","alias_value":"Y5PYV4HAKCON","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"Y5PYV4HAKCON5I22","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"Y5PYV4HA","created_at":"2026-05-18T12:28:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:Y5PYV4HAKCON5I22IRBB2LR3I4","target":"record","payload":{"canonical_record":{"source":{"id":"1410.2164","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-08T15:28:09Z","cross_cats_sorted":[],"title_canon_sha256":"5664562ac9b5cca8b57fae17488cb0880aa38a464cae68cee2fb4d33c025e05f","abstract_canon_sha256":"8ba506c0c6084b49d7b1fcbc69de1ade948dcc75c6e086809a9ede5e21cbc2bb"},"schema_version":"1.0"},"canonical_sha256":"c75f8af0e0509cdea35a44421d2e3b4719c15e45f2ccc81eb76b8d0abe6def29","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:39:39.970262Z","signature_b64":"XDtUlJHtxNHQU854GHGUcXthwkjvpcLRm/iXOnSeEHc+2DyYkdZGJD4JJAj6dXomV2Fns35KT9E2qog6LZGaDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c75f8af0e0509cdea35a44421d2e3b4719c15e45f2ccc81eb76b8d0abe6def29","last_reissued_at":"2026-05-18T02:39:39.969677Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:39:39.969677Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.2164","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":"2026-05-18T02:39:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xJjdJaLkguwTb0WquAQIg0RLa1kRBCzT28F5HI7YZy1zaZxzWpEx354yEeDv2v4bdv6Hxx1x3/cQ0idI+c1XDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T19:08:10.240066Z"},"content_sha256":"ebbf80b8993caf67094cd5c3a62d080cff6b52c95a00fe9362c31f8a1b374091","schema_version":"1.0","event_id":"sha256:ebbf80b8993caf67094cd5c3a62d080cff6b52c95a00fe9362c31f8a1b374091"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:Y5PYV4HAKCON5I22IRBB2LR3I4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A simple arithmetic criterion for graphs being determined by their generalized spectra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Wei Wang","submitted_at":"2014-10-08T15:28:09Z","abstract_excerpt":"A graph $G$ is said to be determined by its generalized spectrum (DGS for short) if for any graph $H$, $H$ and $G$ are cospectral with cospectral complements implies that $H$ is isomorphic to $G$.\n  It turns out that whether a graph $G$ is DGS is closely related to the arithmetic properties of its walk-matrix. More precisely, let $A$ be the adjacency matrix of a graph $G$, and let $W =[e, Ae, A^2e,...,A^{n-1}e]$ ($e$ is the all-one vector) be its \\textit{walk-matrix}. Denote by $\\mathcal{G}_n$ the set of all graphs on $n$ vertices with $\\det(W)\\neq 0$. In [Wang, Generalized spectral characteri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.2164","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":"2026-05-18T02:39:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nSU4Q6ukTCLmBQAqOYfVz6WUUOxMWQ/H97fy4dahlKLHgxlBhC9Ay4abFFbYC+s/mUlVF/5gOAGtYaAFhY/BAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T19:08:10.240792Z"},"content_sha256":"46b0541ddf5abb09c81651c00ade6764c9875061af4addc08eac365eb0734a7a","schema_version":"1.0","event_id":"sha256:46b0541ddf5abb09c81651c00ade6764c9875061af4addc08eac365eb0734a7a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y5PYV4HAKCON5I22IRBB2LR3I4/bundle.json","state_url":"https://pith.science/pith/Y5PYV4HAKCON5I22IRBB2LR3I4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y5PYV4HAKCON5I22IRBB2LR3I4/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":"2026-06-08T19:08:10Z","links":{"resolver":"https://pith.science/pith/Y5PYV4HAKCON5I22IRBB2LR3I4","bundle":"https://pith.science/pith/Y5PYV4HAKCON5I22IRBB2LR3I4/bundle.json","state":"https://pith.science/pith/Y5PYV4HAKCON5I22IRBB2LR3I4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y5PYV4HAKCON5I22IRBB2LR3I4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:Y5PYV4HAKCON5I22IRBB2LR3I4","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":"8ba506c0c6084b49d7b1fcbc69de1ade948dcc75c6e086809a9ede5e21cbc2bb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-08T15:28:09Z","title_canon_sha256":"5664562ac9b5cca8b57fae17488cb0880aa38a464cae68cee2fb4d33c025e05f"},"schema_version":"1.0","source":{"id":"1410.2164","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.2164","created_at":"2026-05-18T02:39:39Z"},{"alias_kind":"arxiv_version","alias_value":"1410.2164v3","created_at":"2026-05-18T02:39:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.2164","created_at":"2026-05-18T02:39:39Z"},{"alias_kind":"pith_short_12","alias_value":"Y5PYV4HAKCON","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"Y5PYV4HAKCON5I22","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"Y5PYV4HA","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:46b0541ddf5abb09c81651c00ade6764c9875061af4addc08eac365eb0734a7a","target":"graph","created_at":"2026-05-18T02:39:39Z","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 graph $G$ is said to be determined by its generalized spectrum (DGS for short) if for any graph $H$, $H$ and $G$ are cospectral with cospectral complements implies that $H$ is isomorphic to $G$.\n  It turns out that whether a graph $G$ is DGS is closely related to the arithmetic properties of its walk-matrix. More precisely, let $A$ be the adjacency matrix of a graph $G$, and let $W =[e, Ae, A^2e,...,A^{n-1}e]$ ($e$ is the all-one vector) be its \\textit{walk-matrix}. Denote by $\\mathcal{G}_n$ the set of all graphs on $n$ vertices with $\\det(W)\\neq 0$. In [Wang, Generalized spectral characteri","authors_text":"Wei Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-08T15:28:09Z","title":"A simple arithmetic criterion for graphs being determined by their generalized spectra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.2164","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:ebbf80b8993caf67094cd5c3a62d080cff6b52c95a00fe9362c31f8a1b374091","target":"record","created_at":"2026-05-18T02:39:39Z","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":"8ba506c0c6084b49d7b1fcbc69de1ade948dcc75c6e086809a9ede5e21cbc2bb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-08T15:28:09Z","title_canon_sha256":"5664562ac9b5cca8b57fae17488cb0880aa38a464cae68cee2fb4d33c025e05f"},"schema_version":"1.0","source":{"id":"1410.2164","kind":"arxiv","version":3}},"canonical_sha256":"c75f8af0e0509cdea35a44421d2e3b4719c15e45f2ccc81eb76b8d0abe6def29","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c75f8af0e0509cdea35a44421d2e3b4719c15e45f2ccc81eb76b8d0abe6def29","first_computed_at":"2026-05-18T02:39:39.969677Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:39.969677Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XDtUlJHtxNHQU854GHGUcXthwkjvpcLRm/iXOnSeEHc+2DyYkdZGJD4JJAj6dXomV2Fns35KT9E2qog6LZGaDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:39.970262Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.2164","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ebbf80b8993caf67094cd5c3a62d080cff6b52c95a00fe9362c31f8a1b374091","sha256:46b0541ddf5abb09c81651c00ade6764c9875061af4addc08eac365eb0734a7a"],"state_sha256":"cb93718d1f1462b18e789391fbfe232bb52944758fc6c0464354f3c176f7c670"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jB5ENKSk75McvU/a1SZr5NHwotlHHVkc7yfOkxFvd2n1xcpIFC2eFm1uTDha4bdRM4UHjRzgPkYHUUtbnwmRBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T19:08:10.244391Z","bundle_sha256":"acb19a7f49b3b751a4355d81666a6038eb2762db1f11877f59f49769d8efa508"}}