{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:CBMSV6SILV77WJFNEVK5FE4C4N","short_pith_number":"pith:CBMSV6SI","canonical_record":{"source":{"id":"2607.14907","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-07-16T12:25:38Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"1dc08c5982305d2673998e93942a6735e23411d144015a801c7b8d45f7339ec3","abstract_canon_sha256":"ab7262043aaa5ab6c9a4f7cabb178ee5589f4ad66d4992db48fdcf955fde05bc"},"schema_version":"1.0"},"canonical_sha256":"10592afa485d7ffb24ad2555d29382e34ceeba976d01ce586ef587f529162fc8","source":{"kind":"arxiv","id":"2607.14907","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.14907","created_at":"2026-07-17T01:21:58Z"},{"alias_kind":"arxiv_version","alias_value":"2607.14907v1","created_at":"2026-07-17T01:21:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.14907","created_at":"2026-07-17T01:21:58Z"},{"alias_kind":"pith_short_12","alias_value":"CBMSV6SILV77","created_at":"2026-07-17T01:21:58Z"},{"alias_kind":"pith_short_16","alias_value":"CBMSV6SILV77WJFN","created_at":"2026-07-17T01:21:58Z"},{"alias_kind":"pith_short_8","alias_value":"CBMSV6SI","created_at":"2026-07-17T01:21:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:CBMSV6SILV77WJFNEVK5FE4C4N","target":"record","payload":{"canonical_record":{"source":{"id":"2607.14907","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-07-16T12:25:38Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"1dc08c5982305d2673998e93942a6735e23411d144015a801c7b8d45f7339ec3","abstract_canon_sha256":"ab7262043aaa5ab6c9a4f7cabb178ee5589f4ad66d4992db48fdcf955fde05bc"},"schema_version":"1.0"},"canonical_sha256":"10592afa485d7ffb24ad2555d29382e34ceeba976d01ce586ef587f529162fc8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-17T01:21:58.170626Z","signature_b64":"2l135F4vIkMy+EvVDI19N9ifaPmgHp1VKDkvN+EVgwxkIPSNTLIcC2o0aZiM0SGzatvT3eMPv+LoEBB5R4YTDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"10592afa485d7ffb24ad2555d29382e34ceeba976d01ce586ef587f529162fc8","last_reissued_at":"2026-07-17T01:21:58.169820Z","signature_status":"signed_v1","first_computed_at":"2026-07-17T01:21:58.169820Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.14907","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":"2026-07-17T01:21:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rcMDRWcZs/pwisHlq+gJH/I7YDJ9kjaahpNRDj8ie53SD+wGzc/G2ToV9jssyyP8n/MSzyhhG+7xGpQmyb70AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T06:51:09.672533Z"},"content_sha256":"c5ae890a5c9855b9b1cc66251d4538e8305e07280d48c10895c48e9ad6286705","schema_version":"1.0","event_id":"sha256:c5ae890a5c9855b9b1cc66251d4538e8305e07280d48c10895c48e9ad6286705"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:CBMSV6SILV77WJFNEVK5FE4C4N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Recognition of algebraic matroids is undecidable","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.CO","authors_text":"Geva Yashfe, Tobias Boege","submitted_at":"2026-07-16T12:25:38Z","abstract_excerpt":"We prove that the recognition problem for algebraic matroids is undecidable. Explicitly, this means that there is no algorithm that takes as input a finite set $S$ and a function $r\\colon\\mathcal{P}(S) \\to \\mathbb{Z}_{\\ge 0}$ (where $\\mathcal{P}(S)$ is the power set) and decides whether there exists a pair of fields $F \\subset K$, and a function $f\\colon S \\to K$, such that for all $A \\subseteq S$: $\\mathrm{tr.deg}_{K/F}(f(A)) = r(A)$.\n  This problem is known to be decidable if the characteristic of the fields involved is constrained to be zero. We prove that it is undecidable if the character"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.14907","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/2607.14907/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":"2026-07-17T01:21:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vyzkTG1+FPG13vjkmrA2U3M6TecoJxsOfwW1/DFWdo+0F4h7AhtLdJsK0YjDkBUmUUaHiwdF8EIendjUKrXADQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T06:51:09.672855Z"},"content_sha256":"c67ce5e45c74f1f2c85557a78645d83b56866da86424f44bed73dcd3a80c0655","schema_version":"1.0","event_id":"sha256:c67ce5e45c74f1f2c85557a78645d83b56866da86424f44bed73dcd3a80c0655"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CBMSV6SILV77WJFNEVK5FE4C4N/bundle.json","state_url":"https://pith.science/pith/CBMSV6SILV77WJFNEVK5FE4C4N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CBMSV6SILV77WJFNEVK5FE4C4N/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":"2026-08-14T06:51:09Z","links":{"resolver":"https://pith.science/pith/CBMSV6SILV77WJFNEVK5FE4C4N","bundle":"https://pith.science/pith/CBMSV6SILV77WJFNEVK5FE4C4N/bundle.json","state":"https://pith.science/pith/CBMSV6SILV77WJFNEVK5FE4C4N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CBMSV6SILV77WJFNEVK5FE4C4N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:CBMSV6SILV77WJFNEVK5FE4C4N","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":"ab7262043aaa5ab6c9a4f7cabb178ee5589f4ad66d4992db48fdcf955fde05bc","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-07-16T12:25:38Z","title_canon_sha256":"1dc08c5982305d2673998e93942a6735e23411d144015a801c7b8d45f7339ec3"},"schema_version":"1.0","source":{"id":"2607.14907","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.14907","created_at":"2026-07-17T01:21:58Z"},{"alias_kind":"arxiv_version","alias_value":"2607.14907v1","created_at":"2026-07-17T01:21:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.14907","created_at":"2026-07-17T01:21:58Z"},{"alias_kind":"pith_short_12","alias_value":"CBMSV6SILV77","created_at":"2026-07-17T01:21:58Z"},{"alias_kind":"pith_short_16","alias_value":"CBMSV6SILV77WJFN","created_at":"2026-07-17T01:21:58Z"},{"alias_kind":"pith_short_8","alias_value":"CBMSV6SI","created_at":"2026-07-17T01:21:58Z"}],"graph_snapshots":[{"event_id":"sha256:c67ce5e45c74f1f2c85557a78645d83b56866da86424f44bed73dcd3a80c0655","target":"graph","created_at":"2026-07-17T01:21:58Z","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/2607.14907/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that the recognition problem for algebraic matroids is undecidable. Explicitly, this means that there is no algorithm that takes as input a finite set $S$ and a function $r\\colon\\mathcal{P}(S) \\to \\mathbb{Z}_{\\ge 0}$ (where $\\mathcal{P}(S)$ is the power set) and decides whether there exists a pair of fields $F \\subset K$, and a function $f\\colon S \\to K$, such that for all $A \\subseteq S$: $\\mathrm{tr.deg}_{K/F}(f(A)) = r(A)$.\n  This problem is known to be decidable if the characteristic of the fields involved is constrained to be zero. We prove that it is undecidable if the character","authors_text":"Geva Yashfe, Tobias Boege","cross_cats":["math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-07-16T12:25:38Z","title":"Recognition of algebraic matroids is undecidable"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.14907","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:c5ae890a5c9855b9b1cc66251d4538e8305e07280d48c10895c48e9ad6286705","target":"record","created_at":"2026-07-17T01:21:58Z","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":"ab7262043aaa5ab6c9a4f7cabb178ee5589f4ad66d4992db48fdcf955fde05bc","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-07-16T12:25:38Z","title_canon_sha256":"1dc08c5982305d2673998e93942a6735e23411d144015a801c7b8d45f7339ec3"},"schema_version":"1.0","source":{"id":"2607.14907","kind":"arxiv","version":1}},"canonical_sha256":"10592afa485d7ffb24ad2555d29382e34ceeba976d01ce586ef587f529162fc8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"10592afa485d7ffb24ad2555d29382e34ceeba976d01ce586ef587f529162fc8","first_computed_at":"2026-07-17T01:21:58.169820Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-17T01:21:58.169820Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2l135F4vIkMy+EvVDI19N9ifaPmgHp1VKDkvN+EVgwxkIPSNTLIcC2o0aZiM0SGzatvT3eMPv+LoEBB5R4YTDA==","signature_status":"signed_v1","signed_at":"2026-07-17T01:21:58.170626Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.14907","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c5ae890a5c9855b9b1cc66251d4538e8305e07280d48c10895c48e9ad6286705","sha256:c67ce5e45c74f1f2c85557a78645d83b56866da86424f44bed73dcd3a80c0655"],"state_sha256":"cd1d184842264342b3913688521814b67d72c3c4e4f81ada6fa9d99b5ccc2dea"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t7FwvWGLz6xOJfCXLuzIHlVl9QHhef73dAGJpEs/Ec1Pc4IrEK13ejm9kNsbG29IikzcY3dLQ4E86HyDwHxGBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T06:51:09.676050Z","bundle_sha256":"bfb88b43ea1de901628d64c9dfe8cd2bc1b9c1074e1f824cde6f9673b3347a26"}}