{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:CO4UN3MNKHU5TYBET7K5DX6FWD","short_pith_number":"pith:CO4UN3MN","canonical_record":{"source":{"id":"2602.24239","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-02-27T18:12:25Z","cross_cats_sorted":[],"title_canon_sha256":"eaa63a45e5643fc8fa4c69d511d9ca96233542fb18167b53d3316211fea02e5d","abstract_canon_sha256":"68fe36d70746e7fabe6c403d0e1a88a770f4143a39fb3b7875fe7dd06b9b72f2"},"schema_version":"1.0"},"canonical_sha256":"13b946ed8d51e9d9e0249fd5d1dfc5b0d3052ec092a5b655c3f2e22a4922bc01","source":{"kind":"arxiv","id":"2602.24239","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.24239","created_at":"2026-06-19T16:11:21Z"},{"alias_kind":"arxiv_version","alias_value":"2602.24239v2","created_at":"2026-06-19T16:11:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.24239","created_at":"2026-06-19T16:11:21Z"},{"alias_kind":"pith_short_12","alias_value":"CO4UN3MNKHU5","created_at":"2026-06-19T16:11:21Z"},{"alias_kind":"pith_short_16","alias_value":"CO4UN3MNKHU5TYBE","created_at":"2026-06-19T16:11:21Z"},{"alias_kind":"pith_short_8","alias_value":"CO4UN3MN","created_at":"2026-06-19T16:11:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:CO4UN3MNKHU5TYBET7K5DX6FWD","target":"record","payload":{"canonical_record":{"source":{"id":"2602.24239","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-02-27T18:12:25Z","cross_cats_sorted":[],"title_canon_sha256":"eaa63a45e5643fc8fa4c69d511d9ca96233542fb18167b53d3316211fea02e5d","abstract_canon_sha256":"68fe36d70746e7fabe6c403d0e1a88a770f4143a39fb3b7875fe7dd06b9b72f2"},"schema_version":"1.0"},"canonical_sha256":"13b946ed8d51e9d9e0249fd5d1dfc5b0d3052ec092a5b655c3f2e22a4922bc01","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:11:21.328614Z","signature_b64":"2j4jr5DZman+YV+oqUR+XhQuvb04qjhV7WTFuQlkiLbB2xmEvo5Ga8a2OMZmj6aEUD5PACpba6U+U2AqMhLkBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"13b946ed8d51e9d9e0249fd5d1dfc5b0d3052ec092a5b655c3f2e22a4922bc01","last_reissued_at":"2026-06-19T16:11:21.328156Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:11:21.328156Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2602.24239","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-19T16:11:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q6n4NakGUoaBRXr4w1ObiqICw3X4Go5gaAYe6EB+5sOIYEq1dERJ6LdswXMXD5xc1cBwP0neyq7JZfHViH/QDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T06:38:53.136410Z"},"content_sha256":"9030480fe4439ea337cf30d6ae696bc5c46fa3d218af7462878afa9ba64812fe","schema_version":"1.0","event_id":"sha256:9030480fe4439ea337cf30d6ae696bc5c46fa3d218af7462878afa9ba64812fe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:CO4UN3MNKHU5TYBET7K5DX6FWD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Diamond Determinants and Somos Sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Nikolai Beluhov","submitted_at":"2026-02-27T18:12:25Z","abstract_excerpt":"A Somos sequence of order $n$ is defined by a quadratic recurrence of width $n + 1$. Some of the remarkable properties of these sequences for small $n$ are tied to certain matrices built out of them being of finite rank. We give an elementary proof of the finite-rank property for order $6$, previously only established with the help of advanced machinery from the theory of hyperelliptic functions. Our method also yields a new finite-rank property for the Somos sequences of order $7$. In addition, we conjecture generalisations of these results to higher orders, for the subclass of Gale-Robinson "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.24239","kind":"arxiv","version":2},"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/2602.24239/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":"2026-06-19T16:11:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fw1eGfR2FR3onRFhdV/WvGyhSvLcZ0S97ivfmXlM9NlSLdeC5NcghuvT0BTzETdi2bwXDilgfO7RALQQzWfZCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T06:38:53.137322Z"},"content_sha256":"87cdc25078050a645fe8fefdcaf3b1f3975fec29872adab8bee7e5efce136e9e","schema_version":"1.0","event_id":"sha256:87cdc25078050a645fe8fefdcaf3b1f3975fec29872adab8bee7e5efce136e9e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CO4UN3MNKHU5TYBET7K5DX6FWD/bundle.json","state_url":"https://pith.science/pith/CO4UN3MNKHU5TYBET7K5DX6FWD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CO4UN3MNKHU5TYBET7K5DX6FWD/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":"2026-08-12T06:38:53Z","links":{"resolver":"https://pith.science/pith/CO4UN3MNKHU5TYBET7K5DX6FWD","bundle":"https://pith.science/pith/CO4UN3MNKHU5TYBET7K5DX6FWD/bundle.json","state":"https://pith.science/pith/CO4UN3MNKHU5TYBET7K5DX6FWD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CO4UN3MNKHU5TYBET7K5DX6FWD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:CO4UN3MNKHU5TYBET7K5DX6FWD","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":"68fe36d70746e7fabe6c403d0e1a88a770f4143a39fb3b7875fe7dd06b9b72f2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-02-27T18:12:25Z","title_canon_sha256":"eaa63a45e5643fc8fa4c69d511d9ca96233542fb18167b53d3316211fea02e5d"},"schema_version":"1.0","source":{"id":"2602.24239","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.24239","created_at":"2026-06-19T16:11:21Z"},{"alias_kind":"arxiv_version","alias_value":"2602.24239v2","created_at":"2026-06-19T16:11:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.24239","created_at":"2026-06-19T16:11:21Z"},{"alias_kind":"pith_short_12","alias_value":"CO4UN3MNKHU5","created_at":"2026-06-19T16:11:21Z"},{"alias_kind":"pith_short_16","alias_value":"CO4UN3MNKHU5TYBE","created_at":"2026-06-19T16:11:21Z"},{"alias_kind":"pith_short_8","alias_value":"CO4UN3MN","created_at":"2026-06-19T16:11:21Z"}],"graph_snapshots":[{"event_id":"sha256:87cdc25078050a645fe8fefdcaf3b1f3975fec29872adab8bee7e5efce136e9e","target":"graph","created_at":"2026-06-19T16:11:21Z","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/2602.24239/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A Somos sequence of order $n$ is defined by a quadratic recurrence of width $n + 1$. Some of the remarkable properties of these sequences for small $n$ are tied to certain matrices built out of them being of finite rank. We give an elementary proof of the finite-rank property for order $6$, previously only established with the help of advanced machinery from the theory of hyperelliptic functions. Our method also yields a new finite-rank property for the Somos sequences of order $7$. In addition, we conjecture generalisations of these results to higher orders, for the subclass of Gale-Robinson ","authors_text":"Nikolai Beluhov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-02-27T18:12:25Z","title":"Diamond Determinants and Somos Sequences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.24239","kind":"arxiv","version":2},"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":"sha256:9030480fe4439ea337cf30d6ae696bc5c46fa3d218af7462878afa9ba64812fe","target":"record","created_at":"2026-06-19T16:11:21Z","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":"68fe36d70746e7fabe6c403d0e1a88a770f4143a39fb3b7875fe7dd06b9b72f2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-02-27T18:12:25Z","title_canon_sha256":"eaa63a45e5643fc8fa4c69d511d9ca96233542fb18167b53d3316211fea02e5d"},"schema_version":"1.0","source":{"id":"2602.24239","kind":"arxiv","version":2}},"canonical_sha256":"13b946ed8d51e9d9e0249fd5d1dfc5b0d3052ec092a5b655c3f2e22a4922bc01","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"13b946ed8d51e9d9e0249fd5d1dfc5b0d3052ec092a5b655c3f2e22a4922bc01","first_computed_at":"2026-06-19T16:11:21.328156Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:11:21.328156Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2j4jr5DZman+YV+oqUR+XhQuvb04qjhV7WTFuQlkiLbB2xmEvo5Ga8a2OMZmj6aEUD5PACpba6U+U2AqMhLkBA==","signature_status":"signed_v1","signed_at":"2026-06-19T16:11:21.328614Z","signed_message":"canonical_sha256_bytes"},"source_id":"2602.24239","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9030480fe4439ea337cf30d6ae696bc5c46fa3d218af7462878afa9ba64812fe","sha256:87cdc25078050a645fe8fefdcaf3b1f3975fec29872adab8bee7e5efce136e9e"],"state_sha256":"d5c5f4eda36e28896715d20fda25781eb593c74a4c4901371da3ec996054362b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FqggLt03CNfJGpOyVxJsk+La5hbKz1QRMMOxD5ShiXogVwM6sflrZ9sWjnI51isZ3fra9u9rO5pwtmw5L8TBCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T06:38:53.148747Z","bundle_sha256":"0123308ec4684072b2a91f5d1a6323a38b2dccb689fc0f733ca51a1a3ad14bc2"}}