{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:6O6QIMQGGOQGAMCRZ42R6WOBE6","short_pith_number":"pith:6O6QIMQG","canonical_record":{"source":{"id":"2411.19883","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2024-11-29T17:48:59Z","cross_cats_sorted":["math.AG","math.CO"],"title_canon_sha256":"80114c52bd2094621df480fc32e0ad30a75a3e881fe920ca3e826468e7f8c8f4","abstract_canon_sha256":"efec6d57634edce9668e42487f6f971c5745433909e69bd2e754b20698cff06b"},"schema_version":"1.0"},"canonical_sha256":"f3bd04320633a0603051cf351f59c12781166b4374636649a756d9464ecbeccd","source":{"kind":"arxiv","id":"2411.19883","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.19883","created_at":"2026-07-05T10:14:25Z"},{"alias_kind":"arxiv_version","alias_value":"2411.19883v3","created_at":"2026-07-05T10:14:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.19883","created_at":"2026-07-05T10:14:25Z"},{"alias_kind":"pith_short_12","alias_value":"6O6QIMQGGOQG","created_at":"2026-07-05T10:14:25Z"},{"alias_kind":"pith_short_16","alias_value":"6O6QIMQGGOQGAMCR","created_at":"2026-07-05T10:14:25Z"},{"alias_kind":"pith_short_8","alias_value":"6O6QIMQG","created_at":"2026-07-05T10:14:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:6O6QIMQGGOQGAMCRZ42R6WOBE6","target":"record","payload":{"canonical_record":{"source":{"id":"2411.19883","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2024-11-29T17:48:59Z","cross_cats_sorted":["math.AG","math.CO"],"title_canon_sha256":"80114c52bd2094621df480fc32e0ad30a75a3e881fe920ca3e826468e7f8c8f4","abstract_canon_sha256":"efec6d57634edce9668e42487f6f971c5745433909e69bd2e754b20698cff06b"},"schema_version":"1.0"},"canonical_sha256":"f3bd04320633a0603051cf351f59c12781166b4374636649a756d9464ecbeccd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:14:25.170152Z","signature_b64":"PbJrZ0Zd7fXoDLeGOAugkyFnbiQrxrCUQy7Fe6S3sf/WxJNck/SjPAHAoboDnU4pZwGgJy7VNPozdNs23/xuCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f3bd04320633a0603051cf351f59c12781166b4374636649a756d9464ecbeccd","last_reissued_at":"2026-07-05T10:14:25.169676Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:14:25.169676Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.19883","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":"2026-07-05T10:14:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xGqm/X1L8dWL17kp2upsx+h6Tgq9Ov1t3u298yMPnMA8OD5BeXh0wdoQN8t9qtNsAWxsPbBwuiS1e2FfeRpXAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T14:58:19.899649Z"},"content_sha256":"b1611cb3f91575b1ac320684ffdd164626c0bede572e47adc0624c070a992a78","schema_version":"1.0","event_id":"sha256:b1611cb3f91575b1ac320684ffdd164626c0bede572e47adc0624c070a992a78"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:6O6QIMQGGOQGAMCRZ42R6WOBE6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Representation theory over semifields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.CO"],"primary_cat":"math.RT","authors_text":"Jaiung Jun, Jeffrey Tolliver, Kalina Mincheva","submitted_at":"2024-11-29T17:48:59Z","abstract_excerpt":"We study and classify representations of a torsion group $G$ over an idempotent semifield with special attention on the case over the Boolean semifield $\\mathbb{B}$. In subsequent work we extend this theory to studying representations of matroids of low rank."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.19883","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.19883/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":"2026-07-05T10:14:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6k8gP/oo1A1+5tU6/yr8NhAjG73REHl1iRKxGIdf/f10GoYKmz83uo3u0+iWZRezLlCM3SfYjvTkOdEjPk9KAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T14:58:19.900717Z"},"content_sha256":"a507ba7bc787df59c4f2bbca92d1a7248e52e813eb940c21ccb7cd7eea096fab","schema_version":"1.0","event_id":"sha256:a507ba7bc787df59c4f2bbca92d1a7248e52e813eb940c21ccb7cd7eea096fab"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6O6QIMQGGOQGAMCRZ42R6WOBE6/bundle.json","state_url":"https://pith.science/pith/6O6QIMQGGOQGAMCRZ42R6WOBE6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6O6QIMQGGOQGAMCRZ42R6WOBE6/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":"2026-08-15T14:58:19Z","links":{"resolver":"https://pith.science/pith/6O6QIMQGGOQGAMCRZ42R6WOBE6","bundle":"https://pith.science/pith/6O6QIMQGGOQGAMCRZ42R6WOBE6/bundle.json","state":"https://pith.science/pith/6O6QIMQGGOQGAMCRZ42R6WOBE6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6O6QIMQGGOQGAMCRZ42R6WOBE6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:6O6QIMQGGOQGAMCRZ42R6WOBE6","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":"efec6d57634edce9668e42487f6f971c5745433909e69bd2e754b20698cff06b","cross_cats_sorted":["math.AG","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2024-11-29T17:48:59Z","title_canon_sha256":"80114c52bd2094621df480fc32e0ad30a75a3e881fe920ca3e826468e7f8c8f4"},"schema_version":"1.0","source":{"id":"2411.19883","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.19883","created_at":"2026-07-05T10:14:25Z"},{"alias_kind":"arxiv_version","alias_value":"2411.19883v3","created_at":"2026-07-05T10:14:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.19883","created_at":"2026-07-05T10:14:25Z"},{"alias_kind":"pith_short_12","alias_value":"6O6QIMQGGOQG","created_at":"2026-07-05T10:14:25Z"},{"alias_kind":"pith_short_16","alias_value":"6O6QIMQGGOQGAMCR","created_at":"2026-07-05T10:14:25Z"},{"alias_kind":"pith_short_8","alias_value":"6O6QIMQG","created_at":"2026-07-05T10:14:25Z"}],"graph_snapshots":[{"event_id":"sha256:a507ba7bc787df59c4f2bbca92d1a7248e52e813eb940c21ccb7cd7eea096fab","target":"graph","created_at":"2026-07-05T10:14:25Z","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/2411.19883/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study and classify representations of a torsion group $G$ over an idempotent semifield with special attention on the case over the Boolean semifield $\\mathbb{B}$. In subsequent work we extend this theory to studying representations of matroids of low rank.","authors_text":"Jaiung Jun, Jeffrey Tolliver, Kalina Mincheva","cross_cats":["math.AG","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2024-11-29T17:48:59Z","title":"Representation theory over semifields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.19883","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:b1611cb3f91575b1ac320684ffdd164626c0bede572e47adc0624c070a992a78","target":"record","created_at":"2026-07-05T10:14:25Z","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":"efec6d57634edce9668e42487f6f971c5745433909e69bd2e754b20698cff06b","cross_cats_sorted":["math.AG","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2024-11-29T17:48:59Z","title_canon_sha256":"80114c52bd2094621df480fc32e0ad30a75a3e881fe920ca3e826468e7f8c8f4"},"schema_version":"1.0","source":{"id":"2411.19883","kind":"arxiv","version":3}},"canonical_sha256":"f3bd04320633a0603051cf351f59c12781166b4374636649a756d9464ecbeccd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f3bd04320633a0603051cf351f59c12781166b4374636649a756d9464ecbeccd","first_computed_at":"2026-07-05T10:14:25.169676Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:14:25.169676Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PbJrZ0Zd7fXoDLeGOAugkyFnbiQrxrCUQy7Fe6S3sf/WxJNck/SjPAHAoboDnU4pZwGgJy7VNPozdNs23/xuCw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:14:25.170152Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.19883","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b1611cb3f91575b1ac320684ffdd164626c0bede572e47adc0624c070a992a78","sha256:a507ba7bc787df59c4f2bbca92d1a7248e52e813eb940c21ccb7cd7eea096fab"],"state_sha256":"1918e9f9ab2991273b70fdc0fdefaae6415567655a7c78b73ee3696d8d1b546e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xi+Ow3Dyaw47ffojMFnRx14wwXYSMRcwrllwbWIT5fCNWZS/aV9y0ia5DcVKg4DeWCA0gWOcN7nmbLSlg2/6AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T14:58:19.906186Z","bundle_sha256":"37185464395254a662335d73a4bfa4422916c1d9314bd6f8072b00c8620a469f"}}