{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:2ZIEVUOBSLLKKNUYHETVGLHRCS","short_pith_number":"pith:2ZIEVUOB","canonical_record":{"source":{"id":"1507.02740","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-07-09T23:21:23Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"672f33ce877eb34d721e3a64ab23cd00a916a211555ecc9c1ca11b608b28f89a","abstract_canon_sha256":"5d505065a6773271ad2977914c3a42f76db47170b9b899f8b8f8fa981077e9a7"},"schema_version":"1.0"},"canonical_sha256":"d6504ad1c192d6a536983927532cf114a50c20b6fda1a8d58432be83aeb7c8e3","source":{"kind":"arxiv","id":"1507.02740","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.02740","created_at":"2026-05-18T00:31:14Z"},{"alias_kind":"arxiv_version","alias_value":"1507.02740v3","created_at":"2026-05-18T00:31:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.02740","created_at":"2026-05-18T00:31:14Z"},{"alias_kind":"pith_short_12","alias_value":"2ZIEVUOBSLLK","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"2ZIEVUOBSLLKKNUY","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"2ZIEVUOB","created_at":"2026-05-18T12:29:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:2ZIEVUOBSLLKKNUYHETVGLHRCS","target":"record","payload":{"canonical_record":{"source":{"id":"1507.02740","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-07-09T23:21:23Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"672f33ce877eb34d721e3a64ab23cd00a916a211555ecc9c1ca11b608b28f89a","abstract_canon_sha256":"5d505065a6773271ad2977914c3a42f76db47170b9b899f8b8f8fa981077e9a7"},"schema_version":"1.0"},"canonical_sha256":"d6504ad1c192d6a536983927532cf114a50c20b6fda1a8d58432be83aeb7c8e3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:14.129470Z","signature_b64":"qxdq940K0Oe2ymtyNHH9tYqsr+X91ZJdLg3rI4CkNlh14jYEkIpxYJroqi9/Z1Osy3U18jOksvv974OKfNSKDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d6504ad1c192d6a536983927532cf114a50c20b6fda1a8d58432be83aeb7c8e3","last_reissued_at":"2026-05-18T00:31:14.128829Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:14.128829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.02740","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:31:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4RumRZMuYBBjZVLXYWvcEmEb1Xk21Echxk4KxBod+bOzZfCj9hsUfEMCl2L1bhWBie2jHz5J6EqfeL/MszhoBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T12:46:30.845359Z"},"content_sha256":"6c8944071fe19340f4f13031024fbfeebc832fdda435c1653a166a1fa4d898f2","schema_version":"1.0","event_id":"sha256:6c8944071fe19340f4f13031024fbfeebc832fdda435c1653a166a1fa4d898f2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:2ZIEVUOBSLLKKNUYHETVGLHRCS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bouquet algebra of toric ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Apostolos Thoma, Marius Vladoiu, Sonja Petrovi\\'c","submitted_at":"2015-07-09T23:21:23Z","abstract_excerpt":"To any toric ideal $I_A$, encoded by an integer matrix $A$, we associate a matroid structure called {\\em the bouquet graph} of $A$ and introduce another toric ideal called {\\em the bouquet ideal} of $A$. We show how these objects capture the essential combinatorial and algebraic information about $I_A$. Passing from the toric ideal to its bouquet ideal reveals a structure that allows us to classify several cases. For example, on the one end of the spectrum, there are ideals that we call {\\em stable}, for which bouquets capture the complexity of various generating sets as well as the minimal fr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02740","kind":"arxiv","version":3},"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":"2026-05-18T00:31:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zhrqfDNcoeyHXXfinXjiehqM8qDO5PXJQ6N3ab5U5HIqN9DdYG0Dxi9FErvWyn3PMJw+DIVdWrO4O8KnzgvVDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T12:46:30.845701Z"},"content_sha256":"cdacb0ff3e45e91e83340a097c72677a68e113af67e8b1135a15f71e08765cf8","schema_version":"1.0","event_id":"sha256:cdacb0ff3e45e91e83340a097c72677a68e113af67e8b1135a15f71e08765cf8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2ZIEVUOBSLLKKNUYHETVGLHRCS/bundle.json","state_url":"https://pith.science/pith/2ZIEVUOBSLLKKNUYHETVGLHRCS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2ZIEVUOBSLLKKNUYHETVGLHRCS/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":"2026-06-01T12:46:30Z","links":{"resolver":"https://pith.science/pith/2ZIEVUOBSLLKKNUYHETVGLHRCS","bundle":"https://pith.science/pith/2ZIEVUOBSLLKKNUYHETVGLHRCS/bundle.json","state":"https://pith.science/pith/2ZIEVUOBSLLKKNUYHETVGLHRCS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2ZIEVUOBSLLKKNUYHETVGLHRCS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:2ZIEVUOBSLLKKNUYHETVGLHRCS","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":"5d505065a6773271ad2977914c3a42f76db47170b9b899f8b8f8fa981077e9a7","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-07-09T23:21:23Z","title_canon_sha256":"672f33ce877eb34d721e3a64ab23cd00a916a211555ecc9c1ca11b608b28f89a"},"schema_version":"1.0","source":{"id":"1507.02740","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.02740","created_at":"2026-05-18T00:31:14Z"},{"alias_kind":"arxiv_version","alias_value":"1507.02740v3","created_at":"2026-05-18T00:31:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.02740","created_at":"2026-05-18T00:31:14Z"},{"alias_kind":"pith_short_12","alias_value":"2ZIEVUOBSLLK","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"2ZIEVUOBSLLKKNUY","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"2ZIEVUOB","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:cdacb0ff3e45e91e83340a097c72677a68e113af67e8b1135a15f71e08765cf8","target":"graph","created_at":"2026-05-18T00:31:14Z","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":"To any toric ideal $I_A$, encoded by an integer matrix $A$, we associate a matroid structure called {\\em the bouquet graph} of $A$ and introduce another toric ideal called {\\em the bouquet ideal} of $A$. We show how these objects capture the essential combinatorial and algebraic information about $I_A$. Passing from the toric ideal to its bouquet ideal reveals a structure that allows us to classify several cases. For example, on the one end of the spectrum, there are ideals that we call {\\em stable}, for which bouquets capture the complexity of various generating sets as well as the minimal fr","authors_text":"Apostolos Thoma, Marius Vladoiu, Sonja Petrovi\\'c","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-07-09T23:21:23Z","title":"Bouquet algebra of toric ideals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02740","kind":"arxiv","version":3},"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":"sha256:6c8944071fe19340f4f13031024fbfeebc832fdda435c1653a166a1fa4d898f2","target":"record","created_at":"2026-05-18T00:31:14Z","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":"5d505065a6773271ad2977914c3a42f76db47170b9b899f8b8f8fa981077e9a7","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-07-09T23:21:23Z","title_canon_sha256":"672f33ce877eb34d721e3a64ab23cd00a916a211555ecc9c1ca11b608b28f89a"},"schema_version":"1.0","source":{"id":"1507.02740","kind":"arxiv","version":3}},"canonical_sha256":"d6504ad1c192d6a536983927532cf114a50c20b6fda1a8d58432be83aeb7c8e3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d6504ad1c192d6a536983927532cf114a50c20b6fda1a8d58432be83aeb7c8e3","first_computed_at":"2026-05-18T00:31:14.128829Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:14.128829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qxdq940K0Oe2ymtyNHH9tYqsr+X91ZJdLg3rI4CkNlh14jYEkIpxYJroqi9/Z1Osy3U18jOksvv974OKfNSKDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:14.129470Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.02740","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6c8944071fe19340f4f13031024fbfeebc832fdda435c1653a166a1fa4d898f2","sha256:cdacb0ff3e45e91e83340a097c72677a68e113af67e8b1135a15f71e08765cf8"],"state_sha256":"2256ad1aefea4cd2973c6b95668036a61cd8901cfc4a939eb74199db6fd26142"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cDLAMjb7krf244/Ok9V2WYWh0B7r0fmzHVFhZQIyfcQ3CYu+RlCCuEqObEL4MrKhRY267sZXm3lR4/iHv0MeBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T12:46:30.847594Z","bundle_sha256":"e16feeaa523ac670df4908e50e114261816535f0d9b28c59d000e15975154571"}}