{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:RMLUVL63P6IZOG2OWPVP3QPMHC","short_pith_number":"pith:RMLUVL63","canonical_record":{"source":{"id":"2608.03097","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-08-04T04:14:05Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"e6d8f59bb87da66bd645e543be2ebb281b1ba1d033c3ad6647fbc99fee49433d","abstract_canon_sha256":"3c84b42c6347e729b123cf564e4a56942e53fb2ff6583edb7a1c0a17739efe3d"},"schema_version":"1.0"},"canonical_sha256":"8b174aafdb7f91971b4eb3eafdc1ec38b40d642d00a2719fce06573db38da5d0","source":{"kind":"arxiv","id":"2608.03097","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.03097","created_at":"2026-08-05T00:45:35Z"},{"alias_kind":"arxiv_version","alias_value":"2608.03097v1","created_at":"2026-08-05T00:45:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.03097","created_at":"2026-08-05T00:45:35Z"},{"alias_kind":"pith_short_12","alias_value":"RMLUVL63P6IZ","created_at":"2026-08-05T00:45:35Z"},{"alias_kind":"pith_short_16","alias_value":"RMLUVL63P6IZOG2O","created_at":"2026-08-05T00:45:35Z"},{"alias_kind":"pith_short_8","alias_value":"RMLUVL63","created_at":"2026-08-05T00:45:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:RMLUVL63P6IZOG2OWPVP3QPMHC","target":"record","payload":{"canonical_record":{"source":{"id":"2608.03097","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-08-04T04:14:05Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"e6d8f59bb87da66bd645e543be2ebb281b1ba1d033c3ad6647fbc99fee49433d","abstract_canon_sha256":"3c84b42c6347e729b123cf564e4a56942e53fb2ff6583edb7a1c0a17739efe3d"},"schema_version":"1.0"},"canonical_sha256":"8b174aafdb7f91971b4eb3eafdc1ec38b40d642d00a2719fce06573db38da5d0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-05T00:45:35.182101Z","signature_b64":"zHNBKSAxbOQN+Tdq9BD3EE7NiYD2ZW70E55G2LHN7gL4eacM+/bk95y0pF30bT55DJcm/bkPQF+KTCvQPnklCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8b174aafdb7f91971b4eb3eafdc1ec38b40d642d00a2719fce06573db38da5d0","last_reissued_at":"2026-08-05T00:45:35.179506Z","signature_status":"signed_v1","first_computed_at":"2026-08-05T00:45:35.179506Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2608.03097","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":"2026-08-05T00:45:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3yEY+yJFWsgXJZ7L15JZo+SCyati1IBvgSlXKOYo7JJYbKkYs7WmjYGtmR/7vB9/NmwyiSjYRVBhY5R6cGZtAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T04:10:45.928673Z"},"content_sha256":"b43d2693cee98b1c738cb1c6ffaddb1a7094c67bede4db54b77b2df1790b66af","schema_version":"1.0","event_id":"sha256:b43d2693cee98b1c738cb1c6ffaddb1a7094c67bede4db54b77b2df1790b66af"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:RMLUVL63P6IZOG2OWPVP3QPMHC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Counting in Vieta graphs over $\\mathbb{F}_p$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Bogdan Nica","submitted_at":"2026-08-04T04:14:05Z","abstract_excerpt":"We introduce and study a finite simple graph of algebraic origin: the Vieta graph on the solution set over $\\mathbb{F}_p$ to a symmetric, multivariate equation which is quadratic in each variable. This construction is a broad generalization of the Markoff graph over $\\mathbb{F}_p$, extensively studied in the recent literature. We give a systematic approach, partly based on quadratic character sums, to the following basic counting questions: how many vertices does a Vieta graph have, and what is the degree distribution? We focus on explicit counts, addressing the low-dimensional cases in three "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.03097","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/2608.03097/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":"2026-08-05T00:45:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FRzDheo0CiuTBZepU1gDkhE1l4xaVppOr5D301C9KbALhY4hHrFMUkZnA7xkXj+0us9/cA2macyP66Bux0hPAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T04:10:45.932785Z"},"content_sha256":"f7e1b7b7669c0d5340eea5a2a4a7046b7b3ebc4cac18c49108ac8427c63b2183","schema_version":"1.0","event_id":"sha256:f7e1b7b7669c0d5340eea5a2a4a7046b7b3ebc4cac18c49108ac8427c63b2183"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RMLUVL63P6IZOG2OWPVP3QPMHC/bundle.json","state_url":"https://pith.science/pith/RMLUVL63P6IZOG2OWPVP3QPMHC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RMLUVL63P6IZOG2OWPVP3QPMHC/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":"2026-08-17T04:10:45Z","links":{"resolver":"https://pith.science/pith/RMLUVL63P6IZOG2OWPVP3QPMHC","bundle":"https://pith.science/pith/RMLUVL63P6IZOG2OWPVP3QPMHC/bundle.json","state":"https://pith.science/pith/RMLUVL63P6IZOG2OWPVP3QPMHC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RMLUVL63P6IZOG2OWPVP3QPMHC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:RMLUVL63P6IZOG2OWPVP3QPMHC","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":"3c84b42c6347e729b123cf564e4a56942e53fb2ff6583edb7a1c0a17739efe3d","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-08-04T04:14:05Z","title_canon_sha256":"e6d8f59bb87da66bd645e543be2ebb281b1ba1d033c3ad6647fbc99fee49433d"},"schema_version":"1.0","source":{"id":"2608.03097","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.03097","created_at":"2026-08-05T00:45:35Z"},{"alias_kind":"arxiv_version","alias_value":"2608.03097v1","created_at":"2026-08-05T00:45:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.03097","created_at":"2026-08-05T00:45:35Z"},{"alias_kind":"pith_short_12","alias_value":"RMLUVL63P6IZ","created_at":"2026-08-05T00:45:35Z"},{"alias_kind":"pith_short_16","alias_value":"RMLUVL63P6IZOG2O","created_at":"2026-08-05T00:45:35Z"},{"alias_kind":"pith_short_8","alias_value":"RMLUVL63","created_at":"2026-08-05T00:45:35Z"}],"graph_snapshots":[{"event_id":"sha256:f7e1b7b7669c0d5340eea5a2a4a7046b7b3ebc4cac18c49108ac8427c63b2183","target":"graph","created_at":"2026-08-05T00:45:35Z","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/2608.03097/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce and study a finite simple graph of algebraic origin: the Vieta graph on the solution set over $\\mathbb{F}_p$ to a symmetric, multivariate equation which is quadratic in each variable. This construction is a broad generalization of the Markoff graph over $\\mathbb{F}_p$, extensively studied in the recent literature. We give a systematic approach, partly based on quadratic character sums, to the following basic counting questions: how many vertices does a Vieta graph have, and what is the degree distribution? We focus on explicit counts, addressing the low-dimensional cases in three ","authors_text":"Bogdan Nica","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-08-04T04:14:05Z","title":"Counting in Vieta graphs over $\\mathbb{F}_p$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.03097","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:b43d2693cee98b1c738cb1c6ffaddb1a7094c67bede4db54b77b2df1790b66af","target":"record","created_at":"2026-08-05T00:45:35Z","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":"3c84b42c6347e729b123cf564e4a56942e53fb2ff6583edb7a1c0a17739efe3d","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-08-04T04:14:05Z","title_canon_sha256":"e6d8f59bb87da66bd645e543be2ebb281b1ba1d033c3ad6647fbc99fee49433d"},"schema_version":"1.0","source":{"id":"2608.03097","kind":"arxiv","version":1}},"canonical_sha256":"8b174aafdb7f91971b4eb3eafdc1ec38b40d642d00a2719fce06573db38da5d0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8b174aafdb7f91971b4eb3eafdc1ec38b40d642d00a2719fce06573db38da5d0","first_computed_at":"2026-08-05T00:45:35.179506Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-05T00:45:35.179506Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zHNBKSAxbOQN+Tdq9BD3EE7NiYD2ZW70E55G2LHN7gL4eacM+/bk95y0pF30bT55DJcm/bkPQF+KTCvQPnklCA==","signature_status":"signed_v1","signed_at":"2026-08-05T00:45:35.182101Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.03097","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b43d2693cee98b1c738cb1c6ffaddb1a7094c67bede4db54b77b2df1790b66af","sha256:f7e1b7b7669c0d5340eea5a2a4a7046b7b3ebc4cac18c49108ac8427c63b2183"],"state_sha256":"60c2995019d920b367d15b32a5709215ab3f87be49281faf7b213fd7a8c683a7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Eur3hagVh8CmPXLLkYhwqJNk4FtJNZQRZ9ih33vb/AC8OpC8zsxcN3UFsF39gQVc/gnXcBBd0mLo4w07cadUCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T04:10:45.944594Z","bundle_sha256":"43605f338203ae7101cfb33f86abe38f817aa766f106db6508e3ecaf79fd4882"}}