{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:TZPXCRTEFMFPLDPKTZ7KRKSDBV","short_pith_number":"pith:TZPXCRTE","canonical_record":{"source":{"id":"2308.04475","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-08-08T14:37:25Z","cross_cats_sorted":[],"title_canon_sha256":"a7bf44055fd02e85b949bdea612f422f36b54217c95e9f42e22af1dc9bb64b39","abstract_canon_sha256":"488f68bc45764f80342402489169a646e2a650c6de093f4e8b09af28c22c96d0"},"schema_version":"1.0"},"canonical_sha256":"9e5f7146642b0af58dea9e7ea8aa430d5d366b6b0025b9a6fb93b54b7f1843ad","source":{"kind":"arxiv","id":"2308.04475","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2308.04475","created_at":"2026-07-05T06:39:38Z"},{"alias_kind":"arxiv_version","alias_value":"2308.04475v1","created_at":"2026-07-05T06:39:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.04475","created_at":"2026-07-05T06:39:38Z"},{"alias_kind":"pith_short_12","alias_value":"TZPXCRTEFMFP","created_at":"2026-07-05T06:39:38Z"},{"alias_kind":"pith_short_16","alias_value":"TZPXCRTEFMFPLDPK","created_at":"2026-07-05T06:39:38Z"},{"alias_kind":"pith_short_8","alias_value":"TZPXCRTE","created_at":"2026-07-05T06:39:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:TZPXCRTEFMFPLDPKTZ7KRKSDBV","target":"record","payload":{"canonical_record":{"source":{"id":"2308.04475","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-08-08T14:37:25Z","cross_cats_sorted":[],"title_canon_sha256":"a7bf44055fd02e85b949bdea612f422f36b54217c95e9f42e22af1dc9bb64b39","abstract_canon_sha256":"488f68bc45764f80342402489169a646e2a650c6de093f4e8b09af28c22c96d0"},"schema_version":"1.0"},"canonical_sha256":"9e5f7146642b0af58dea9e7ea8aa430d5d366b6b0025b9a6fb93b54b7f1843ad","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:39:38.540985Z","signature_b64":"oU4YM+bkYYCdEh7Xb+d6DfATqxAkMykDIxpiK7CMFr9Wl+IY50IduKeSGDuIcYLz53vs+LiyIk+hzQ/3unSSCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9e5f7146642b0af58dea9e7ea8aa430d5d366b6b0025b9a6fb93b54b7f1843ad","last_reissued_at":"2026-07-05T06:39:38.540559Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:39:38.540559Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2308.04475","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":"2026-07-05T06:39:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fkP72oRfAKpX1wIuqFTSs2rJsOT9PYaTwGQpBBQ98dygPknRqREkUTokxEdPsMe20mKa+DfuysKZlw8f4OUMCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T13:55:13.153771Z"},"content_sha256":"ccee05b7862002af88e16575f310282c2c7768ce15f80c3c22e4c5561a7516e6","schema_version":"1.0","event_id":"sha256:ccee05b7862002af88e16575f310282c2c7768ce15f80c3c22e4c5561a7516e6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:TZPXCRTEFMFPLDPKTZ7KRKSDBV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sums of squares of eigenvalues and the vector chromatic number","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Gabriel Coutinho, Thom\\'as Jung Spier","submitted_at":"2023-08-08T14:37:25Z","abstract_excerpt":"In this short paper we prove that the sum of the squares of negative (or positive) eigenvalues of the adjacency matrix of a graph is lower bounded by the sum of the degrees divided by the vector chromatic number, resolving a conjecture by Wocjan, Elphick and Anekstein (2018)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.04475","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/2308.04475/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":"2026-07-05T06:39:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cxud8CgZUL1aTBvWgBBv3w1zDsogHNYahSQUX7qgtXwE+rrhVwUl1IJ8W6Q8tFs390JrfdqDMTVxKD7AGRIDBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T13:55:13.154284Z"},"content_sha256":"3a1ac3c8b3835b9c41405cb567f7b332e45f876c10666cb2f21e64231e225a18","schema_version":"1.0","event_id":"sha256:3a1ac3c8b3835b9c41405cb567f7b332e45f876c10666cb2f21e64231e225a18"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TZPXCRTEFMFPLDPKTZ7KRKSDBV/bundle.json","state_url":"https://pith.science/pith/TZPXCRTEFMFPLDPKTZ7KRKSDBV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TZPXCRTEFMFPLDPKTZ7KRKSDBV/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":"2026-08-09T13:55:13Z","links":{"resolver":"https://pith.science/pith/TZPXCRTEFMFPLDPKTZ7KRKSDBV","bundle":"https://pith.science/pith/TZPXCRTEFMFPLDPKTZ7KRKSDBV/bundle.json","state":"https://pith.science/pith/TZPXCRTEFMFPLDPKTZ7KRKSDBV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TZPXCRTEFMFPLDPKTZ7KRKSDBV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:TZPXCRTEFMFPLDPKTZ7KRKSDBV","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":"488f68bc45764f80342402489169a646e2a650c6de093f4e8b09af28c22c96d0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-08-08T14:37:25Z","title_canon_sha256":"a7bf44055fd02e85b949bdea612f422f36b54217c95e9f42e22af1dc9bb64b39"},"schema_version":"1.0","source":{"id":"2308.04475","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2308.04475","created_at":"2026-07-05T06:39:38Z"},{"alias_kind":"arxiv_version","alias_value":"2308.04475v1","created_at":"2026-07-05T06:39:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.04475","created_at":"2026-07-05T06:39:38Z"},{"alias_kind":"pith_short_12","alias_value":"TZPXCRTEFMFP","created_at":"2026-07-05T06:39:38Z"},{"alias_kind":"pith_short_16","alias_value":"TZPXCRTEFMFPLDPK","created_at":"2026-07-05T06:39:38Z"},{"alias_kind":"pith_short_8","alias_value":"TZPXCRTE","created_at":"2026-07-05T06:39:38Z"}],"graph_snapshots":[{"event_id":"sha256:3a1ac3c8b3835b9c41405cb567f7b332e45f876c10666cb2f21e64231e225a18","target":"graph","created_at":"2026-07-05T06:39:38Z","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/2308.04475/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this short paper we prove that the sum of the squares of negative (or positive) eigenvalues of the adjacency matrix of a graph is lower bounded by the sum of the degrees divided by the vector chromatic number, resolving a conjecture by Wocjan, Elphick and Anekstein (2018).","authors_text":"Gabriel Coutinho, Thom\\'as Jung Spier","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-08-08T14:37:25Z","title":"Sums of squares of eigenvalues and the vector chromatic number"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.04475","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:ccee05b7862002af88e16575f310282c2c7768ce15f80c3c22e4c5561a7516e6","target":"record","created_at":"2026-07-05T06:39:38Z","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":"488f68bc45764f80342402489169a646e2a650c6de093f4e8b09af28c22c96d0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-08-08T14:37:25Z","title_canon_sha256":"a7bf44055fd02e85b949bdea612f422f36b54217c95e9f42e22af1dc9bb64b39"},"schema_version":"1.0","source":{"id":"2308.04475","kind":"arxiv","version":1}},"canonical_sha256":"9e5f7146642b0af58dea9e7ea8aa430d5d366b6b0025b9a6fb93b54b7f1843ad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9e5f7146642b0af58dea9e7ea8aa430d5d366b6b0025b9a6fb93b54b7f1843ad","first_computed_at":"2026-07-05T06:39:38.540559Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:39:38.540559Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oU4YM+bkYYCdEh7Xb+d6DfATqxAkMykDIxpiK7CMFr9Wl+IY50IduKeSGDuIcYLz53vs+LiyIk+hzQ/3unSSCA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:39:38.540985Z","signed_message":"canonical_sha256_bytes"},"source_id":"2308.04475","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ccee05b7862002af88e16575f310282c2c7768ce15f80c3c22e4c5561a7516e6","sha256:3a1ac3c8b3835b9c41405cb567f7b332e45f876c10666cb2f21e64231e225a18"],"state_sha256":"4463819665d122106888495d6ec31fd6ff94032b995fea4e39904fde8dee95e3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CvtGBXTP9tBAJB7mE6dtKl246d0b4LzjBN2A5z53otUPWA7k/pBKkW8JlxTwUO0ZgWgIt7VJU0vo0kmAcHZhDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T13:55:13.158080Z","bundle_sha256":"47dd68de053a32625f07eba38dd7d19e4281115d0a389901e83729b9c1e2553e"}}