{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:PNTEWHD2EAWVRHNR7DJG4QMAEU","short_pith_number":"pith:PNTEWHD2","canonical_record":{"source":{"id":"2606.24339","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-06-23T09:25:12Z","cross_cats_sorted":[],"title_canon_sha256":"cb4d4d9c3d81f502dcc22e6aa1cc9e3f5d42e50d549c0650bd6b7c513772f2f7","abstract_canon_sha256":"99fdbf51520b028d4894493c1fd18e57ae83756f281e74fb448a3b726bcdde59"},"schema_version":"1.0"},"canonical_sha256":"7b664b1c7a202d589db1f8d26e41802506f2c24419c93b4a3cdb500fab28d156","source":{"kind":"arxiv","id":"2606.24339","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.24339","created_at":"2026-06-24T01:15:27Z"},{"alias_kind":"arxiv_version","alias_value":"2606.24339v1","created_at":"2026-06-24T01:15:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.24339","created_at":"2026-06-24T01:15:27Z"},{"alias_kind":"pith_short_12","alias_value":"PNTEWHD2EAWV","created_at":"2026-06-24T01:15:27Z"},{"alias_kind":"pith_short_16","alias_value":"PNTEWHD2EAWVRHNR","created_at":"2026-06-24T01:15:27Z"},{"alias_kind":"pith_short_8","alias_value":"PNTEWHD2","created_at":"2026-06-24T01:15:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:PNTEWHD2EAWVRHNR7DJG4QMAEU","target":"record","payload":{"canonical_record":{"source":{"id":"2606.24339","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-06-23T09:25:12Z","cross_cats_sorted":[],"title_canon_sha256":"cb4d4d9c3d81f502dcc22e6aa1cc9e3f5d42e50d549c0650bd6b7c513772f2f7","abstract_canon_sha256":"99fdbf51520b028d4894493c1fd18e57ae83756f281e74fb448a3b726bcdde59"},"schema_version":"1.0"},"canonical_sha256":"7b664b1c7a202d589db1f8d26e41802506f2c24419c93b4a3cdb500fab28d156","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-24T01:15:27.596888Z","signature_b64":"ijPms7QbG+SPVVVdeVWLqNfq4clj/00ubBSCpiU4RrISv2SrdBqe8aGEr1jRcH/sFCPa8ELw6LQ+6/aYHHkYAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7b664b1c7a202d589db1f8d26e41802506f2c24419c93b4a3cdb500fab28d156","last_reissued_at":"2026-06-24T01:15:27.596432Z","signature_status":"signed_v1","first_computed_at":"2026-06-24T01:15:27.596432Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.24339","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":"2026-06-24T01:15:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DTk7j28EySH1t1EK6Qbqf9wuYGbUE/zNLv45vBHqPaIXQZe8r2bJ1o9FvbhSl9btcB6SpMpyN+TRjLYwsH0GAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T21:41:22.138394Z"},"content_sha256":"cd532ae34792c489ea2254762b1b993787c1d1245b8c819a80827aed2c7a7013","schema_version":"1.0","event_id":"sha256:cd532ae34792c489ea2254762b1b993787c1d1245b8c819a80827aed2c7a7013"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:PNTEWHD2EAWVRHNR7DJG4QMAEU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Toward a classification of tropical complete intersection number one","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Linxuan Li","submitted_at":"2026-06-23T09:25:12Z","abstract_excerpt":"By bridging two classification results -- the Esterov--Gusev classification of tuples of lattice polytopes of mixed volume one, and Fink's characterization of Bergman fans -- we formulate a classification conjecture describing when the stable intersection of a tropical fan F with the tropicalization Trop(X) of a subvariety of T^n is a reduced point. Our main results establish this conjecture in three fundamental cases -- unmixed sequences, hypersurface complete-intersection cycles, and tropical 2-cycles -- and develop several tools intended for the general case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.24339","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/2606.24339/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":"2026-06-24T01:15:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QA41zQ5FCWHalRBYMblEDbFnzmrfkuShZ3km/C5FlaLmlGxLwzGmo7raksPu4WK98jGmG4UqrShl/47JEwEEAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T21:41:22.138899Z"},"content_sha256":"e1cb1ffe37dde901f93f1129e04b2560edae01afd26a88a55bb241d728520e8d","schema_version":"1.0","event_id":"sha256:e1cb1ffe37dde901f93f1129e04b2560edae01afd26a88a55bb241d728520e8d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PNTEWHD2EAWVRHNR7DJG4QMAEU/bundle.json","state_url":"https://pith.science/pith/PNTEWHD2EAWVRHNR7DJG4QMAEU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PNTEWHD2EAWVRHNR7DJG4QMAEU/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":"2026-08-10T21:41:22Z","links":{"resolver":"https://pith.science/pith/PNTEWHD2EAWVRHNR7DJG4QMAEU","bundle":"https://pith.science/pith/PNTEWHD2EAWVRHNR7DJG4QMAEU/bundle.json","state":"https://pith.science/pith/PNTEWHD2EAWVRHNR7DJG4QMAEU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PNTEWHD2EAWVRHNR7DJG4QMAEU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:PNTEWHD2EAWVRHNR7DJG4QMAEU","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":"99fdbf51520b028d4894493c1fd18e57ae83756f281e74fb448a3b726bcdde59","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-06-23T09:25:12Z","title_canon_sha256":"cb4d4d9c3d81f502dcc22e6aa1cc9e3f5d42e50d549c0650bd6b7c513772f2f7"},"schema_version":"1.0","source":{"id":"2606.24339","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.24339","created_at":"2026-06-24T01:15:27Z"},{"alias_kind":"arxiv_version","alias_value":"2606.24339v1","created_at":"2026-06-24T01:15:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.24339","created_at":"2026-06-24T01:15:27Z"},{"alias_kind":"pith_short_12","alias_value":"PNTEWHD2EAWV","created_at":"2026-06-24T01:15:27Z"},{"alias_kind":"pith_short_16","alias_value":"PNTEWHD2EAWVRHNR","created_at":"2026-06-24T01:15:27Z"},{"alias_kind":"pith_short_8","alias_value":"PNTEWHD2","created_at":"2026-06-24T01:15:27Z"}],"graph_snapshots":[{"event_id":"sha256:e1cb1ffe37dde901f93f1129e04b2560edae01afd26a88a55bb241d728520e8d","target":"graph","created_at":"2026-06-24T01:15:27Z","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/2606.24339/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"By bridging two classification results -- the Esterov--Gusev classification of tuples of lattice polytopes of mixed volume one, and Fink's characterization of Bergman fans -- we formulate a classification conjecture describing when the stable intersection of a tropical fan F with the tropicalization Trop(X) of a subvariety of T^n is a reduced point. Our main results establish this conjecture in three fundamental cases -- unmixed sequences, hypersurface complete-intersection cycles, and tropical 2-cycles -- and develop several tools intended for the general case.","authors_text":"Linxuan Li","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-06-23T09:25:12Z","title":"Toward a classification of tropical complete intersection number one"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.24339","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:cd532ae34792c489ea2254762b1b993787c1d1245b8c819a80827aed2c7a7013","target":"record","created_at":"2026-06-24T01:15:27Z","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":"99fdbf51520b028d4894493c1fd18e57ae83756f281e74fb448a3b726bcdde59","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-06-23T09:25:12Z","title_canon_sha256":"cb4d4d9c3d81f502dcc22e6aa1cc9e3f5d42e50d549c0650bd6b7c513772f2f7"},"schema_version":"1.0","source":{"id":"2606.24339","kind":"arxiv","version":1}},"canonical_sha256":"7b664b1c7a202d589db1f8d26e41802506f2c24419c93b4a3cdb500fab28d156","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7b664b1c7a202d589db1f8d26e41802506f2c24419c93b4a3cdb500fab28d156","first_computed_at":"2026-06-24T01:15:27.596432Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-24T01:15:27.596432Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ijPms7QbG+SPVVVdeVWLqNfq4clj/00ubBSCpiU4RrISv2SrdBqe8aGEr1jRcH/sFCPa8ELw6LQ+6/aYHHkYAw==","signature_status":"signed_v1","signed_at":"2026-06-24T01:15:27.596888Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.24339","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd532ae34792c489ea2254762b1b993787c1d1245b8c819a80827aed2c7a7013","sha256:e1cb1ffe37dde901f93f1129e04b2560edae01afd26a88a55bb241d728520e8d"],"state_sha256":"fb24ff4f5fea3ff1c87715e1b05c5dc222981e32df889fe4583005d85f3617b4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rkqfkLTPSKNiKKxqECaw94PcrsfgsKvYgHJBqLtNRPgvdkGvQV8heu8m9CjE98wVlKQHlbmpsHoEKWBoNulnBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T21:41:22.144486Z","bundle_sha256":"adb2b48236ff4644946b7b963ff385c404ca06fec427052f90ce0cd049ec7595"}}