{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:ZARYCODBZI444VAKG2VVJJC3PN","short_pith_number":"pith:ZARYCODB","canonical_record":{"source":{"id":"2607.18334","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-07-19T17:33:48Z","cross_cats_sorted":["cs.DM","math.SP"],"title_canon_sha256":"2a6e5189dd0e8c569339ecfd1bc089094d64b01e041190c1170cbd8d334ada40","abstract_canon_sha256":"74d26b858241b89ff80699d12b8269b25f7cc3c7390783400ca4a089798f9698"},"schema_version":"1.0"},"canonical_sha256":"c823813861ca39ce540a36ab54a45b7b64e44694c51b7c4e251b41f379896230","source":{"kind":"arxiv","id":"2607.18334","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.18334","created_at":"2026-07-22T00:22:42Z"},{"alias_kind":"arxiv_version","alias_value":"2607.18334v1","created_at":"2026-07-22T00:22:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.18334","created_at":"2026-07-22T00:22:42Z"},{"alias_kind":"pith_short_12","alias_value":"ZARYCODBZI44","created_at":"2026-07-22T00:22:42Z"},{"alias_kind":"pith_short_16","alias_value":"ZARYCODBZI444VAK","created_at":"2026-07-22T00:22:42Z"},{"alias_kind":"pith_short_8","alias_value":"ZARYCODB","created_at":"2026-07-22T00:22:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:ZARYCODBZI444VAKG2VVJJC3PN","target":"record","payload":{"canonical_record":{"source":{"id":"2607.18334","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-07-19T17:33:48Z","cross_cats_sorted":["cs.DM","math.SP"],"title_canon_sha256":"2a6e5189dd0e8c569339ecfd1bc089094d64b01e041190c1170cbd8d334ada40","abstract_canon_sha256":"74d26b858241b89ff80699d12b8269b25f7cc3c7390783400ca4a089798f9698"},"schema_version":"1.0"},"canonical_sha256":"c823813861ca39ce540a36ab54a45b7b64e44694c51b7c4e251b41f379896230","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-22T00:22:42.239765Z","signature_b64":"zxKDiv+FPGOnQBh3edHqy/OJ7yHPuTzhmjfKgUUnBfpReprfVfjiphOj0qVIfgxnsY+IfcZwvjcnY2/E3HuyDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c823813861ca39ce540a36ab54a45b7b64e44694c51b7c4e251b41f379896230","last_reissued_at":"2026-07-22T00:22:42.238946Z","signature_status":"signed_v1","first_computed_at":"2026-07-22T00:22:42.238946Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.18334","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":"2026-07-22T00:22:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TlHx3Yt1QJ4JHM4r0AJR95yA9MlSfdsxP/Se3OUONNlmcbV8/sE/myMFRNgYJbXzS8dmbziZFmB5mUFFzoVKAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T06:34:26.704671Z"},"content_sha256":"7ed80c0df8fe2d072505972e0147acc391a9599e1785e8d5b9c723d03d0fca3d","schema_version":"1.0","event_id":"sha256:7ed80c0df8fe2d072505972e0147acc391a9599e1785e8d5b9c723d03d0fca3d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:ZARYCODBZI444VAKG2VVJJC3PN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Signed circulants at the Ramanujan bound","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.SP"],"primary_cat":"math.CO","authors_text":"Vaibhav Suvagiya","submitted_at":"2026-07-19T17:33:48Z","abstract_excerpt":"For the circulant graph $C_n(1,2)$ with $n\\ge10$ even, the $\\F_2$ system requiring every quadrilateral to be unbalanced is consistent and its solutions form exactly four switching classes. We show that the class containing the signing which is $+1$ on step-$1$ edges and $(-1)^i$ on step-$2$ edges has spectrum $\\{\\pm2\\sqrt{\\cos^2\\theta_k+\\cos^2 2\\theta_k}\\}$ and spectral radius exactly $2\\sqrt2$, well below the Kesten bound $2\\sqrt3$; that the quadrilateral system is equivalent to alternating triangle fluxes, so that the four classes are coordinatized by $(\\tau_0,\\alpha)$ and the spectral radiu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.18334","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/2607.18334/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":"2026-07-22T00:22:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+3F9pfJxEzcon+fJQaOUYZCmavIsWU2kOvKmwKeqz0VHzmCfgLCszDnqKBVHCsZywZ7wBeXzNpGly9xLllrKCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T06:34:26.705175Z"},"content_sha256":"c1f6a227a5d880e0e4671c6f0a245af8eb2505c3a2e17798fec7da3daa46a618","schema_version":"1.0","event_id":"sha256:c1f6a227a5d880e0e4671c6f0a245af8eb2505c3a2e17798fec7da3daa46a618"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZARYCODBZI444VAKG2VVJJC3PN/bundle.json","state_url":"https://pith.science/pith/ZARYCODBZI444VAKG2VVJJC3PN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZARYCODBZI444VAKG2VVJJC3PN/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":"2026-08-12T06:34:26Z","links":{"resolver":"https://pith.science/pith/ZARYCODBZI444VAKG2VVJJC3PN","bundle":"https://pith.science/pith/ZARYCODBZI444VAKG2VVJJC3PN/bundle.json","state":"https://pith.science/pith/ZARYCODBZI444VAKG2VVJJC3PN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZARYCODBZI444VAKG2VVJJC3PN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:ZARYCODBZI444VAKG2VVJJC3PN","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":"74d26b858241b89ff80699d12b8269b25f7cc3c7390783400ca4a089798f9698","cross_cats_sorted":["cs.DM","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-07-19T17:33:48Z","title_canon_sha256":"2a6e5189dd0e8c569339ecfd1bc089094d64b01e041190c1170cbd8d334ada40"},"schema_version":"1.0","source":{"id":"2607.18334","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.18334","created_at":"2026-07-22T00:22:42Z"},{"alias_kind":"arxiv_version","alias_value":"2607.18334v1","created_at":"2026-07-22T00:22:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.18334","created_at":"2026-07-22T00:22:42Z"},{"alias_kind":"pith_short_12","alias_value":"ZARYCODBZI44","created_at":"2026-07-22T00:22:42Z"},{"alias_kind":"pith_short_16","alias_value":"ZARYCODBZI444VAK","created_at":"2026-07-22T00:22:42Z"},{"alias_kind":"pith_short_8","alias_value":"ZARYCODB","created_at":"2026-07-22T00:22:42Z"}],"graph_snapshots":[{"event_id":"sha256:c1f6a227a5d880e0e4671c6f0a245af8eb2505c3a2e17798fec7da3daa46a618","target":"graph","created_at":"2026-07-22T00:22:42Z","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/2607.18334/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For the circulant graph $C_n(1,2)$ with $n\\ge10$ even, the $\\F_2$ system requiring every quadrilateral to be unbalanced is consistent and its solutions form exactly four switching classes. We show that the class containing the signing which is $+1$ on step-$1$ edges and $(-1)^i$ on step-$2$ edges has spectrum $\\{\\pm2\\sqrt{\\cos^2\\theta_k+\\cos^2 2\\theta_k}\\}$ and spectral radius exactly $2\\sqrt2$, well below the Kesten bound $2\\sqrt3$; that the quadrilateral system is equivalent to alternating triangle fluxes, so that the four classes are coordinatized by $(\\tau_0,\\alpha)$ and the spectral radiu","authors_text":"Vaibhav Suvagiya","cross_cats":["cs.DM","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-07-19T17:33:48Z","title":"Signed circulants at the Ramanujan bound"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.18334","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":"sha256:7ed80c0df8fe2d072505972e0147acc391a9599e1785e8d5b9c723d03d0fca3d","target":"record","created_at":"2026-07-22T00:22:42Z","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":"74d26b858241b89ff80699d12b8269b25f7cc3c7390783400ca4a089798f9698","cross_cats_sorted":["cs.DM","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-07-19T17:33:48Z","title_canon_sha256":"2a6e5189dd0e8c569339ecfd1bc089094d64b01e041190c1170cbd8d334ada40"},"schema_version":"1.0","source":{"id":"2607.18334","kind":"arxiv","version":1}},"canonical_sha256":"c823813861ca39ce540a36ab54a45b7b64e44694c51b7c4e251b41f379896230","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c823813861ca39ce540a36ab54a45b7b64e44694c51b7c4e251b41f379896230","first_computed_at":"2026-07-22T00:22:42.238946Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-22T00:22:42.238946Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zxKDiv+FPGOnQBh3edHqy/OJ7yHPuTzhmjfKgUUnBfpReprfVfjiphOj0qVIfgxnsY+IfcZwvjcnY2/E3HuyDA==","signature_status":"signed_v1","signed_at":"2026-07-22T00:22:42.239765Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.18334","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7ed80c0df8fe2d072505972e0147acc391a9599e1785e8d5b9c723d03d0fca3d","sha256:c1f6a227a5d880e0e4671c6f0a245af8eb2505c3a2e17798fec7da3daa46a618"],"state_sha256":"752ec2c66894df6e8cc98bd2b0e82783f9172bde85355d44cf478e6e05a82ae9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mm7uaQQxhXU93PTqp7SOyFL8/FncyC5atBsBy8WFKv0hKtWcqTcjTphlwbcPLTdPq717H3shU7+B54DiepckAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T06:34:26.709195Z","bundle_sha256":"62d8f38fcd984198bb26802e0caf23ff4d66ead2f2f088aa2f94deee546c19d9"}}