{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:ELQAHNI6OBAVOKT5LQY4V5SAUP","short_pith_number":"pith:ELQAHNI6","canonical_record":{"source":{"id":"2607.05835","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-07-07T04:56:22Z","cross_cats_sorted":["cs.AI","math.CO"],"title_canon_sha256":"cbeb53e86e3ed65f0a33df34e50abf5c536f1ec272181027b9b07c28c7ce9b40","abstract_canon_sha256":"05245054687120c201c88a982e055b0f4fd201e1fabbbba4a6721433e6dbcbaf"},"schema_version":"1.0"},"canonical_sha256":"22e003b51e7041572a7d5c31caf640a3ee1877995b74b87e0802f555da3a9944","source":{"kind":"arxiv","id":"2607.05835","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.05835","created_at":"2026-07-08T01:18:47Z"},{"alias_kind":"arxiv_version","alias_value":"2607.05835v1","created_at":"2026-07-08T01:18:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.05835","created_at":"2026-07-08T01:18:47Z"},{"alias_kind":"pith_short_12","alias_value":"ELQAHNI6OBAV","created_at":"2026-07-08T01:18:47Z"},{"alias_kind":"pith_short_16","alias_value":"ELQAHNI6OBAVOKT5","created_at":"2026-07-08T01:18:47Z"},{"alias_kind":"pith_short_8","alias_value":"ELQAHNI6","created_at":"2026-07-08T01:18:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:ELQAHNI6OBAVOKT5LQY4V5SAUP","target":"record","payload":{"canonical_record":{"source":{"id":"2607.05835","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-07-07T04:56:22Z","cross_cats_sorted":["cs.AI","math.CO"],"title_canon_sha256":"cbeb53e86e3ed65f0a33df34e50abf5c536f1ec272181027b9b07c28c7ce9b40","abstract_canon_sha256":"05245054687120c201c88a982e055b0f4fd201e1fabbbba4a6721433e6dbcbaf"},"schema_version":"1.0"},"canonical_sha256":"22e003b51e7041572a7d5c31caf640a3ee1877995b74b87e0802f555da3a9944","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-08T01:18:47.666754Z","signature_b64":"NCeflFZKXIxfXZzMoimHY+4b0aPC7clY3EkpTBIOcNc0aLtHBjdV0AxnZry7NxvSqyry1MoUmFL4rzekkFOmCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"22e003b51e7041572a7d5c31caf640a3ee1877995b74b87e0802f555da3a9944","last_reissued_at":"2026-07-08T01:18:47.666078Z","signature_status":"signed_v1","first_computed_at":"2026-07-08T01:18:47.666078Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.05835","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":"2026-07-08T01:18:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"puSpzClfn4XDiSePWO7QcdEfG5NDwo9g+wZyDVm3npm/PxysTcjMVf8TDpt9tjwPqMVT9xDJZ/nDL0VJpgsoBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T21:43:31.596987Z"},"content_sha256":"e56792ccc5503145e0839df018b3d3f80e1feff34bf5ce066f9d99ba031e27e2","schema_version":"1.0","event_id":"sha256:e56792ccc5503145e0839df018b3d3f80e1feff34bf5ce066f9d99ba031e27e2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:ELQAHNI6OBAVOKT5LQY4V5SAUP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tangent classes of matroids and wonderful compactifications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","math.CO"],"primary_cat":"math.AG","authors_text":"Guoxiong Gao, Ronnie Cheng, Shurui Liu","submitted_at":"2026-07-07T04:56:22Z","abstract_excerpt":"For every loopless matroid $M$ and every Feichtner--Yuzvinsky building set $\\mathcal{G}$ containing the top flat, we construct an integral tangent class $T_{M,\\mathcal{G}}^{\\mathbb{Z}}\\in K_{\\mathbb{Z}}(M,\\mathcal{G})$; in the realizable case it specializes to the class of the tangent bundle of the corresponding wonderful compactification, it recovers the Hilbert series of the Chow ring through Hirzebruch--Riemann--Roch, and it satisfies the expected Chern-alpha lower bounds. This reproduces the tangent class and its key properties studied by the first author in arXiv:2606.22650. The main body"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.05835","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/2607.05835/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":"2026-07-08T01:18:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Cm4e7sb7th4b0byKufuAtvwcw36NKre5LYMa4X6z+i8Cerl+EEEpmTDIXdh5uD5P97AYJ1ytPahbbp/f3WnSDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T21:43:31.597497Z"},"content_sha256":"deab3371069bab4298609faf941ceef2cbf0a6c0f261bdf3e341dfac6773b967","schema_version":"1.0","event_id":"sha256:deab3371069bab4298609faf941ceef2cbf0a6c0f261bdf3e341dfac6773b967"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ELQAHNI6OBAVOKT5LQY4V5SAUP/bundle.json","state_url":"https://pith.science/pith/ELQAHNI6OBAVOKT5LQY4V5SAUP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ELQAHNI6OBAVOKT5LQY4V5SAUP/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":"2026-08-03T21:43:31Z","links":{"resolver":"https://pith.science/pith/ELQAHNI6OBAVOKT5LQY4V5SAUP","bundle":"https://pith.science/pith/ELQAHNI6OBAVOKT5LQY4V5SAUP/bundle.json","state":"https://pith.science/pith/ELQAHNI6OBAVOKT5LQY4V5SAUP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ELQAHNI6OBAVOKT5LQY4V5SAUP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:ELQAHNI6OBAVOKT5LQY4V5SAUP","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":"05245054687120c201c88a982e055b0f4fd201e1fabbbba4a6721433e6dbcbaf","cross_cats_sorted":["cs.AI","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-07-07T04:56:22Z","title_canon_sha256":"cbeb53e86e3ed65f0a33df34e50abf5c536f1ec272181027b9b07c28c7ce9b40"},"schema_version":"1.0","source":{"id":"2607.05835","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.05835","created_at":"2026-07-08T01:18:47Z"},{"alias_kind":"arxiv_version","alias_value":"2607.05835v1","created_at":"2026-07-08T01:18:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.05835","created_at":"2026-07-08T01:18:47Z"},{"alias_kind":"pith_short_12","alias_value":"ELQAHNI6OBAV","created_at":"2026-07-08T01:18:47Z"},{"alias_kind":"pith_short_16","alias_value":"ELQAHNI6OBAVOKT5","created_at":"2026-07-08T01:18:47Z"},{"alias_kind":"pith_short_8","alias_value":"ELQAHNI6","created_at":"2026-07-08T01:18:47Z"}],"graph_snapshots":[{"event_id":"sha256:deab3371069bab4298609faf941ceef2cbf0a6c0f261bdf3e341dfac6773b967","target":"graph","created_at":"2026-07-08T01:18:47Z","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/2607.05835/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For every loopless matroid $M$ and every Feichtner--Yuzvinsky building set $\\mathcal{G}$ containing the top flat, we construct an integral tangent class $T_{M,\\mathcal{G}}^{\\mathbb{Z}}\\in K_{\\mathbb{Z}}(M,\\mathcal{G})$; in the realizable case it specializes to the class of the tangent bundle of the corresponding wonderful compactification, it recovers the Hilbert series of the Chow ring through Hirzebruch--Riemann--Roch, and it satisfies the expected Chern-alpha lower bounds. This reproduces the tangent class and its key properties studied by the first author in arXiv:2606.22650. The main body","authors_text":"Guoxiong Gao, Ronnie Cheng, Shurui Liu","cross_cats":["cs.AI","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-07-07T04:56:22Z","title":"Tangent classes of matroids and wonderful compactifications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.05835","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:e56792ccc5503145e0839df018b3d3f80e1feff34bf5ce066f9d99ba031e27e2","target":"record","created_at":"2026-07-08T01:18:47Z","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":"05245054687120c201c88a982e055b0f4fd201e1fabbbba4a6721433e6dbcbaf","cross_cats_sorted":["cs.AI","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-07-07T04:56:22Z","title_canon_sha256":"cbeb53e86e3ed65f0a33df34e50abf5c536f1ec272181027b9b07c28c7ce9b40"},"schema_version":"1.0","source":{"id":"2607.05835","kind":"arxiv","version":1}},"canonical_sha256":"22e003b51e7041572a7d5c31caf640a3ee1877995b74b87e0802f555da3a9944","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"22e003b51e7041572a7d5c31caf640a3ee1877995b74b87e0802f555da3a9944","first_computed_at":"2026-07-08T01:18:47.666078Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-08T01:18:47.666078Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NCeflFZKXIxfXZzMoimHY+4b0aPC7clY3EkpTBIOcNc0aLtHBjdV0AxnZry7NxvSqyry1MoUmFL4rzekkFOmCA==","signature_status":"signed_v1","signed_at":"2026-07-08T01:18:47.666754Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.05835","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e56792ccc5503145e0839df018b3d3f80e1feff34bf5ce066f9d99ba031e27e2","sha256:deab3371069bab4298609faf941ceef2cbf0a6c0f261bdf3e341dfac6773b967"],"state_sha256":"2e8c803298fbd503405c39e7225d1762aa6e59cc52501f406cbffccc25acc163"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KHdTssqYKmg6zJ6/RJHcDchPcP4Pi80oaRPhXGbfaZPb5QfUyyc4fqWuhpVaIa3vfnYR9qzE69H/wWhIq2tyDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T21:43:31.601186Z","bundle_sha256":"1dd2461749b29730f196e54f8abaddd5f51ca4a22a84ced758033c892932c0b0"}}