{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:VBX5KB5HJQN55BXBUVSDZN4B76","short_pith_number":"pith:VBX5KB5H","canonical_record":{"source":{"id":"2508.17332","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2025-08-24T12:40:26Z","cross_cats_sorted":["math-ph","math.CO","math.MP"],"title_canon_sha256":"6efb5545cb9a8b1ded6a27c203d130c69a98b1ff19cfc146a1b20d2c4e6c360d","abstract_canon_sha256":"49ee948151b18a883012851e04c4b1a8df7e75b0d3b0b608b4c0650ab30b4d59"},"schema_version":"1.0"},"canonical_sha256":"a86fd507a74c1bde86e1a5643cb781ffbcec22f268974a271ad7133a829209af","source":{"kind":"arxiv","id":"2508.17332","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.17332","created_at":"2026-07-05T11:58:39Z"},{"alias_kind":"arxiv_version","alias_value":"2508.17332v1","created_at":"2026-07-05T11:58:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.17332","created_at":"2026-07-05T11:58:39Z"},{"alias_kind":"pith_short_12","alias_value":"VBX5KB5HJQN5","created_at":"2026-07-05T11:58:39Z"},{"alias_kind":"pith_short_16","alias_value":"VBX5KB5HJQN55BXB","created_at":"2026-07-05T11:58:39Z"},{"alias_kind":"pith_short_8","alias_value":"VBX5KB5H","created_at":"2026-07-05T11:58:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:VBX5KB5HJQN55BXBUVSDZN4B76","target":"record","payload":{"canonical_record":{"source":{"id":"2508.17332","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2025-08-24T12:40:26Z","cross_cats_sorted":["math-ph","math.CO","math.MP"],"title_canon_sha256":"6efb5545cb9a8b1ded6a27c203d130c69a98b1ff19cfc146a1b20d2c4e6c360d","abstract_canon_sha256":"49ee948151b18a883012851e04c4b1a8df7e75b0d3b0b608b4c0650ab30b4d59"},"schema_version":"1.0"},"canonical_sha256":"a86fd507a74c1bde86e1a5643cb781ffbcec22f268974a271ad7133a829209af","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:58:39.989261Z","signature_b64":"EjSvLLHvZZ1KoB67XBzQPyJAoUQNo+rXL8Y+4FhH14aEm3rcThG9aQCCJ/npmIZiubAHrMk0VYEu6mce1Q/OBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a86fd507a74c1bde86e1a5643cb781ffbcec22f268974a271ad7133a829209af","last_reissued_at":"2026-07-05T11:58:39.988817Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:58:39.988817Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2508.17332","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":"2026-07-05T11:58:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eSCUx9nwz0Tu1XK/BWvIidtLqNf98wC1+lH/YYFegRUK2/61QxlVpxiK/WL5zVVcVs3jg/HPszDi3c19m14ZDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T03:06:53.661698Z"},"content_sha256":"e0e41eba8ab0fc8dceb273fbc947201133d44a1c97fdc95b75c6e70a62a4c03c","schema_version":"1.0","event_id":"sha256:e0e41eba8ab0fc8dceb273fbc947201133d44a1c97fdc95b75c6e70a62a4c03c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:VBX5KB5HJQN55BXBUVSDZN4B76","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Eigenvalues of Maximal Abelian Covers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CO","math.MP"],"primary_cat":"math.SP","authors_text":"Joe Thomas, Michael Magee, Mostafa Sabri, Wenbo Li","submitted_at":"2025-08-24T12:40:26Z","abstract_excerpt":"We fully characterize the eigenvalues (flat bands) of the maximal abelian cover of a finite multi-graph in terms of the combinatorics of the base graph. This solves a problem of Higuchi and Nomura (2009, Problem 6.11). We use our new criterion to prove that the maximal abelian cover of any regular multi-graph has no eigenvalues, thereby proving a conjecture of (ibid., Conjecture 6.12). In an appendix, we relate our criterion for eigenvalues of the maximal abelian cover to an existing criterion for eigenvalues of the universal cover."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.17332","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/2508.17332/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":"2026-07-05T11:58:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HNqrk1kQJ9bun6UzTGXdc4HzUi36W0KRapCqf3b9j3UC+z6PM3W/yVCKT1Ixce18pbEHrjpqLxewvtWaF5yQBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T03:06:53.662355Z"},"content_sha256":"37739424f326670b5eb78b9de7c92c3c9f673ff8bde43cefb62b4aed1091da99","schema_version":"1.0","event_id":"sha256:37739424f326670b5eb78b9de7c92c3c9f673ff8bde43cefb62b4aed1091da99"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VBX5KB5HJQN55BXBUVSDZN4B76/bundle.json","state_url":"https://pith.science/pith/VBX5KB5HJQN55BXBUVSDZN4B76/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VBX5KB5HJQN55BXBUVSDZN4B76/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":"2026-08-21T03:06:53Z","links":{"resolver":"https://pith.science/pith/VBX5KB5HJQN55BXBUVSDZN4B76","bundle":"https://pith.science/pith/VBX5KB5HJQN55BXBUVSDZN4B76/bundle.json","state":"https://pith.science/pith/VBX5KB5HJQN55BXBUVSDZN4B76/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VBX5KB5HJQN55BXBUVSDZN4B76/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:VBX5KB5HJQN55BXBUVSDZN4B76","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":"49ee948151b18a883012851e04c4b1a8df7e75b0d3b0b608b4c0650ab30b4d59","cross_cats_sorted":["math-ph","math.CO","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2025-08-24T12:40:26Z","title_canon_sha256":"6efb5545cb9a8b1ded6a27c203d130c69a98b1ff19cfc146a1b20d2c4e6c360d"},"schema_version":"1.0","source":{"id":"2508.17332","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.17332","created_at":"2026-07-05T11:58:39Z"},{"alias_kind":"arxiv_version","alias_value":"2508.17332v1","created_at":"2026-07-05T11:58:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.17332","created_at":"2026-07-05T11:58:39Z"},{"alias_kind":"pith_short_12","alias_value":"VBX5KB5HJQN5","created_at":"2026-07-05T11:58:39Z"},{"alias_kind":"pith_short_16","alias_value":"VBX5KB5HJQN55BXB","created_at":"2026-07-05T11:58:39Z"},{"alias_kind":"pith_short_8","alias_value":"VBX5KB5H","created_at":"2026-07-05T11:58:39Z"}],"graph_snapshots":[{"event_id":"sha256:37739424f326670b5eb78b9de7c92c3c9f673ff8bde43cefb62b4aed1091da99","target":"graph","created_at":"2026-07-05T11:58:39Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2508.17332/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We fully characterize the eigenvalues (flat bands) of the maximal abelian cover of a finite multi-graph in terms of the combinatorics of the base graph. This solves a problem of Higuchi and Nomura (2009, Problem 6.11). We use our new criterion to prove that the maximal abelian cover of any regular multi-graph has no eigenvalues, thereby proving a conjecture of (ibid., Conjecture 6.12). In an appendix, we relate our criterion for eigenvalues of the maximal abelian cover to an existing criterion for eigenvalues of the universal cover.","authors_text":"Joe Thomas, Michael Magee, Mostafa Sabri, Wenbo Li","cross_cats":["math-ph","math.CO","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2025-08-24T12:40:26Z","title":"Eigenvalues of Maximal Abelian Covers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.17332","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:e0e41eba8ab0fc8dceb273fbc947201133d44a1c97fdc95b75c6e70a62a4c03c","target":"record","created_at":"2026-07-05T11:58:39Z","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":"49ee948151b18a883012851e04c4b1a8df7e75b0d3b0b608b4c0650ab30b4d59","cross_cats_sorted":["math-ph","math.CO","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2025-08-24T12:40:26Z","title_canon_sha256":"6efb5545cb9a8b1ded6a27c203d130c69a98b1ff19cfc146a1b20d2c4e6c360d"},"schema_version":"1.0","source":{"id":"2508.17332","kind":"arxiv","version":1}},"canonical_sha256":"a86fd507a74c1bde86e1a5643cb781ffbcec22f268974a271ad7133a829209af","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a86fd507a74c1bde86e1a5643cb781ffbcec22f268974a271ad7133a829209af","first_computed_at":"2026-07-05T11:58:39.988817Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:58:39.988817Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EjSvLLHvZZ1KoB67XBzQPyJAoUQNo+rXL8Y+4FhH14aEm3rcThG9aQCCJ/npmIZiubAHrMk0VYEu6mce1Q/OBw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:58:39.989261Z","signed_message":"canonical_sha256_bytes"},"source_id":"2508.17332","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e0e41eba8ab0fc8dceb273fbc947201133d44a1c97fdc95b75c6e70a62a4c03c","sha256:37739424f326670b5eb78b9de7c92c3c9f673ff8bde43cefb62b4aed1091da99"],"state_sha256":"e04173480a57dd425f30197136214141c18f1da4808ceb8933244d7b000325c2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kZhwvUlLM3GKJLd8nVMAoMSeNUvrJzOsFVPTILLbJPgwgfVQzVpwW7TcXzQYAPe77H+qnyZATHrRULxS+yq0Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T03:06:53.666633Z","bundle_sha256":"a89ac2b20be6f92079a76779be92e7de66974010ed3b4f6bfc8ce44bff2b02b0"}}