{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:AA5CZFQNVSSIII6NHVPDOJIENC","short_pith_number":"pith:AA5CZFQN","canonical_record":{"source":{"id":"0706.0009","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2007-05-31T20:17:36Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"032a7529f06db09038b42c5ac7610bb38022db99f1b802633b5da364c31cef62","abstract_canon_sha256":"58005a4d081353e678a77be50507d4b1594b549d5eb4f4a264c67a8db757236e"},"schema_version":"1.0"},"canonical_sha256":"003a2c960daca48423cd3d5e37250468af86813584143e70bec51f1c97d8ea7f","source":{"kind":"arxiv","id":"0706.0009","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0706.0009","created_at":"2026-05-18T02:59:45Z"},{"alias_kind":"arxiv_version","alias_value":"0706.0009v2","created_at":"2026-05-18T02:59:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0706.0009","created_at":"2026-05-18T02:59:45Z"},{"alias_kind":"pith_short_12","alias_value":"AA5CZFQNVSSI","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"AA5CZFQNVSSIII6N","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"AA5CZFQN","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:AA5CZFQNVSSIII6NHVPDOJIENC","target":"record","payload":{"canonical_record":{"source":{"id":"0706.0009","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2007-05-31T20:17:36Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"032a7529f06db09038b42c5ac7610bb38022db99f1b802633b5da364c31cef62","abstract_canon_sha256":"58005a4d081353e678a77be50507d4b1594b549d5eb4f4a264c67a8db757236e"},"schema_version":"1.0"},"canonical_sha256":"003a2c960daca48423cd3d5e37250468af86813584143e70bec51f1c97d8ea7f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:59:45.828277Z","signature_b64":"H4OCMnYPW0Ba0BcO7HFF126xpCq8fdTrQrsTrQkQC7y7Xnqhvjxpksh9YkIa7Ld6h9iQ+80NTLeCAcGHPPGoCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"003a2c960daca48423cd3d5e37250468af86813584143e70bec51f1c97d8ea7f","last_reissued_at":"2026-05-18T02:59:45.827801Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:59:45.827801Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0706.0009","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":"2026-05-18T02:59:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w32FFZ5cLLIkxq/c391V1fhHoVbUTPBSoVXCHh+/5ezQ9jwz5M8k/qhWireUxbz5T/4eiKsLKFo3KfNGwCPqDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T22:24:02.864447Z"},"content_sha256":"d7c9110f1048e154c3b8f56338f12f0220ccee22cc87a96b14821b61022b51fe","schema_version":"1.0","event_id":"sha256:d7c9110f1048e154c3b8f56338f12f0220ccee22cc87a96b14821b61022b51fe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:AA5CZFQNVSSIII6NHVPDOJIENC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exponents of 2-multiarrangements and multiplicity lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CO","authors_text":"Takuro Abe, Yasuhide Numata","submitted_at":"2007-05-31T20:17:36Z","abstract_excerpt":"We introduce a concept of multiplicity lattices of 2-multiarrangements, determine the combinatorics and geometry of that lattice, and give a criterion and method to construct a basis for derivation modules effectively."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.0009","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":""},"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":"2026-05-18T02:59:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IpxxHG+oefBf2LPRt8n+dRbz8vA+6Zz/pMC26u8G7e6MWQeIk30RzJCDMfvnvWmz3bLHkC9rQ0lYYvE7e6k1Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T22:24:02.864879Z"},"content_sha256":"86c4f753261812a3d8889510b749052ce944da95c4e8ecdfe68258d187d0cd9b","schema_version":"1.0","event_id":"sha256:86c4f753261812a3d8889510b749052ce944da95c4e8ecdfe68258d187d0cd9b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AA5CZFQNVSSIII6NHVPDOJIENC/bundle.json","state_url":"https://pith.science/pith/AA5CZFQNVSSIII6NHVPDOJIENC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AA5CZFQNVSSIII6NHVPDOJIENC/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":"2026-05-27T22:24:02Z","links":{"resolver":"https://pith.science/pith/AA5CZFQNVSSIII6NHVPDOJIENC","bundle":"https://pith.science/pith/AA5CZFQNVSSIII6NHVPDOJIENC/bundle.json","state":"https://pith.science/pith/AA5CZFQNVSSIII6NHVPDOJIENC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AA5CZFQNVSSIII6NHVPDOJIENC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:AA5CZFQNVSSIII6NHVPDOJIENC","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":"58005a4d081353e678a77be50507d4b1594b549d5eb4f4a264c67a8db757236e","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2007-05-31T20:17:36Z","title_canon_sha256":"032a7529f06db09038b42c5ac7610bb38022db99f1b802633b5da364c31cef62"},"schema_version":"1.0","source":{"id":"0706.0009","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0706.0009","created_at":"2026-05-18T02:59:45Z"},{"alias_kind":"arxiv_version","alias_value":"0706.0009v2","created_at":"2026-05-18T02:59:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0706.0009","created_at":"2026-05-18T02:59:45Z"},{"alias_kind":"pith_short_12","alias_value":"AA5CZFQNVSSI","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"AA5CZFQNVSSIII6N","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"AA5CZFQN","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:86c4f753261812a3d8889510b749052ce944da95c4e8ecdfe68258d187d0cd9b","target":"graph","created_at":"2026-05-18T02:59:45Z","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"},"paper":{"abstract_excerpt":"We introduce a concept of multiplicity lattices of 2-multiarrangements, determine the combinatorics and geometry of that lattice, and give a criterion and method to construct a basis for derivation modules effectively.","authors_text":"Takuro Abe, Yasuhide Numata","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2007-05-31T20:17:36Z","title":"Exponents of 2-multiarrangements and multiplicity lattices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.0009","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:d7c9110f1048e154c3b8f56338f12f0220ccee22cc87a96b14821b61022b51fe","target":"record","created_at":"2026-05-18T02:59:45Z","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":"58005a4d081353e678a77be50507d4b1594b549d5eb4f4a264c67a8db757236e","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2007-05-31T20:17:36Z","title_canon_sha256":"032a7529f06db09038b42c5ac7610bb38022db99f1b802633b5da364c31cef62"},"schema_version":"1.0","source":{"id":"0706.0009","kind":"arxiv","version":2}},"canonical_sha256":"003a2c960daca48423cd3d5e37250468af86813584143e70bec51f1c97d8ea7f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"003a2c960daca48423cd3d5e37250468af86813584143e70bec51f1c97d8ea7f","first_computed_at":"2026-05-18T02:59:45.827801Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:59:45.827801Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"H4OCMnYPW0Ba0BcO7HFF126xpCq8fdTrQrsTrQkQC7y7Xnqhvjxpksh9YkIa7Ld6h9iQ+80NTLeCAcGHPPGoCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:59:45.828277Z","signed_message":"canonical_sha256_bytes"},"source_id":"0706.0009","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d7c9110f1048e154c3b8f56338f12f0220ccee22cc87a96b14821b61022b51fe","sha256:86c4f753261812a3d8889510b749052ce944da95c4e8ecdfe68258d187d0cd9b"],"state_sha256":"d096b119b8006f2e422aaec6e758cc7c379d835e752d10c547fa8db6c50300e0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YgX9gwVJARemIni0N6xVbP2F0M9hFV9V/Ad/cWNjhbRdOhzWwsgRWY7ALeaB+cvSp2rl79uI2ZFMftZNJGUMAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T22:24:02.867918Z","bundle_sha256":"f3b5e40b58f8e12434e466f18f351f4a8d608624beada99646d5fe042879cee5"}}