{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:SCQYH42GDMPOZQFOOGRAYWZ3DD","short_pith_number":"pith:SCQYH42G","canonical_record":{"source":{"id":"2507.06365","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-07-08T19:57:59Z","cross_cats_sorted":[],"title_canon_sha256":"5d245d28be01b4a4a451568460d2765870242730694c113aff4992c0c3a0c1a8","abstract_canon_sha256":"b7892a4fb4654c129662a07e369e45d72aa08d8649b91c02760f3a5371bcf56c"},"schema_version":"1.0"},"canonical_sha256":"90a183f3461b1eecc0ae71a20c5b3b18c1ee82a428ffe843a5ac0f494bd1e19d","source":{"kind":"arxiv","id":"2507.06365","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.06365","created_at":"2026-07-05T11:34:14Z"},{"alias_kind":"arxiv_version","alias_value":"2507.06365v1","created_at":"2026-07-05T11:34:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.06365","created_at":"2026-07-05T11:34:14Z"},{"alias_kind":"pith_short_12","alias_value":"SCQYH42GDMPO","created_at":"2026-07-05T11:34:14Z"},{"alias_kind":"pith_short_16","alias_value":"SCQYH42GDMPOZQFO","created_at":"2026-07-05T11:34:14Z"},{"alias_kind":"pith_short_8","alias_value":"SCQYH42G","created_at":"2026-07-05T11:34:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:SCQYH42GDMPOZQFOOGRAYWZ3DD","target":"record","payload":{"canonical_record":{"source":{"id":"2507.06365","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-07-08T19:57:59Z","cross_cats_sorted":[],"title_canon_sha256":"5d245d28be01b4a4a451568460d2765870242730694c113aff4992c0c3a0c1a8","abstract_canon_sha256":"b7892a4fb4654c129662a07e369e45d72aa08d8649b91c02760f3a5371bcf56c"},"schema_version":"1.0"},"canonical_sha256":"90a183f3461b1eecc0ae71a20c5b3b18c1ee82a428ffe843a5ac0f494bd1e19d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:34:14.392370Z","signature_b64":"RzbhwCvnygOsM0jVYjpUzLmVYNd1noK/iOrc8LPftBrA3EnpTlBBkuAjM7wVpU/I2myR2wDzXIxdxAfghjGqCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"90a183f3461b1eecc0ae71a20c5b3b18c1ee82a428ffe843a5ac0f494bd1e19d","last_reissued_at":"2026-07-05T11:34:14.391971Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:34:14.391971Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2507.06365","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":"2026-07-05T11:34:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gEgGDc9UcEj6bxlmr8MHbxGaA0oZDAKw8HOvF+gllVpTsvRDaJntDDiww0wjsNi3J9UjY0EgWZqbmxZuHC+rAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-09T03:11:03.751395Z"},"content_sha256":"4d4c333319e756fc087fbc8c895128aaa185899c140adbbeb07490e262f57316","schema_version":"1.0","event_id":"sha256:4d4c333319e756fc087fbc8c895128aaa185899c140adbbeb07490e262f57316"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:SCQYH42GDMPOZQFOOGRAYWZ3DD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Salvetti complexes for conditional oriented matroids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dan Dugger, Galen Dorpalen-Barry, Nicholas Proudfoot","submitted_at":"2025-07-08T19:57:59Z","abstract_excerpt":"We give a new proof of the fact that the complement of the complexification of a real hyperplane arrangement is homotopy equivalent to the Salvetti complex of the associated oriented matroid. Our proof involves no choices, is relatively easy to visualize, and generalizes to the setting of conditional oriented matroids."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.06365","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/2507.06365/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":"2026-07-05T11:34:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"39k8DQX2RK/zheaFFgb31d3yWOTb3421/AGGAR2BVUEa6C9fCAEpHO9TEgx0Yd3KAFLi5A7qz7ZW1tKfc5OTDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-09T03:11:03.752132Z"},"content_sha256":"d0bb3a67a85f0199aa693caae4fbee093e6299994e51050a1f0b58365f536da9","schema_version":"1.0","event_id":"sha256:d0bb3a67a85f0199aa693caae4fbee093e6299994e51050a1f0b58365f536da9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SCQYH42GDMPOZQFOOGRAYWZ3DD/bundle.json","state_url":"https://pith.science/pith/SCQYH42GDMPOZQFOOGRAYWZ3DD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SCQYH42GDMPOZQFOOGRAYWZ3DD/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":"2026-07-09T03:11:03Z","links":{"resolver":"https://pith.science/pith/SCQYH42GDMPOZQFOOGRAYWZ3DD","bundle":"https://pith.science/pith/SCQYH42GDMPOZQFOOGRAYWZ3DD/bundle.json","state":"https://pith.science/pith/SCQYH42GDMPOZQFOOGRAYWZ3DD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SCQYH42GDMPOZQFOOGRAYWZ3DD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:SCQYH42GDMPOZQFOOGRAYWZ3DD","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":"b7892a4fb4654c129662a07e369e45d72aa08d8649b91c02760f3a5371bcf56c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-07-08T19:57:59Z","title_canon_sha256":"5d245d28be01b4a4a451568460d2765870242730694c113aff4992c0c3a0c1a8"},"schema_version":"1.0","source":{"id":"2507.06365","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.06365","created_at":"2026-07-05T11:34:14Z"},{"alias_kind":"arxiv_version","alias_value":"2507.06365v1","created_at":"2026-07-05T11:34:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.06365","created_at":"2026-07-05T11:34:14Z"},{"alias_kind":"pith_short_12","alias_value":"SCQYH42GDMPO","created_at":"2026-07-05T11:34:14Z"},{"alias_kind":"pith_short_16","alias_value":"SCQYH42GDMPOZQFO","created_at":"2026-07-05T11:34:14Z"},{"alias_kind":"pith_short_8","alias_value":"SCQYH42G","created_at":"2026-07-05T11:34:14Z"}],"graph_snapshots":[{"event_id":"sha256:d0bb3a67a85f0199aa693caae4fbee093e6299994e51050a1f0b58365f536da9","target":"graph","created_at":"2026-07-05T11:34:14Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2507.06365/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We give a new proof of the fact that the complement of the complexification of a real hyperplane arrangement is homotopy equivalent to the Salvetti complex of the associated oriented matroid. Our proof involves no choices, is relatively easy to visualize, and generalizes to the setting of conditional oriented matroids.","authors_text":"Dan Dugger, Galen Dorpalen-Barry, Nicholas Proudfoot","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-07-08T19:57:59Z","title":"Salvetti complexes for conditional oriented matroids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.06365","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":"sha256:4d4c333319e756fc087fbc8c895128aaa185899c140adbbeb07490e262f57316","target":"record","created_at":"2026-07-05T11:34:14Z","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":"b7892a4fb4654c129662a07e369e45d72aa08d8649b91c02760f3a5371bcf56c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-07-08T19:57:59Z","title_canon_sha256":"5d245d28be01b4a4a451568460d2765870242730694c113aff4992c0c3a0c1a8"},"schema_version":"1.0","source":{"id":"2507.06365","kind":"arxiv","version":1}},"canonical_sha256":"90a183f3461b1eecc0ae71a20c5b3b18c1ee82a428ffe843a5ac0f494bd1e19d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"90a183f3461b1eecc0ae71a20c5b3b18c1ee82a428ffe843a5ac0f494bd1e19d","first_computed_at":"2026-07-05T11:34:14.391971Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:34:14.391971Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RzbhwCvnygOsM0jVYjpUzLmVYNd1noK/iOrc8LPftBrA3EnpTlBBkuAjM7wVpU/I2myR2wDzXIxdxAfghjGqCw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:34:14.392370Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.06365","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4d4c333319e756fc087fbc8c895128aaa185899c140adbbeb07490e262f57316","sha256:d0bb3a67a85f0199aa693caae4fbee093e6299994e51050a1f0b58365f536da9"],"state_sha256":"35af131e12c308a760afcff8ff32b4dac43aca7cd873cb6d82548015c19f04a8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5ejY/jTdrLJq6kmZtzoR0X2pTfcd+h0xOz6sisuJuFmL0NtmWShLmoiSkcezj3Cl27ZZ3wEjsb53SlMN6+FPBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-09T03:11:03.755244Z","bundle_sha256":"cc675be7d41aaadbe0332a4366778c3a0243a8744f671181789da8ab2897c6c1"}}