{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:6IPMWJHWB23JGAECV4PD5ENDSH","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":"9a165d73b977a834e3baace959fa1705fd7fdc07011e57c0fe1694fccf875e9e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2026-06-24T17:13:53Z","title_canon_sha256":"06791d82406cb68420c7468b6cad6ba7f0d02bb22b07638763539f01f3e90a65"},"schema_version":"1.0","source":{"id":"2606.26038","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.26038","created_at":"2026-06-25T01:18:46Z"},{"alias_kind":"arxiv_version","alias_value":"2606.26038v1","created_at":"2026-06-25T01:18:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.26038","created_at":"2026-06-25T01:18:46Z"},{"alias_kind":"pith_short_12","alias_value":"6IPMWJHWB23J","created_at":"2026-06-25T01:18:46Z"},{"alias_kind":"pith_short_16","alias_value":"6IPMWJHWB23JGAEC","created_at":"2026-06-25T01:18:46Z"},{"alias_kind":"pith_short_8","alias_value":"6IPMWJHW","created_at":"2026-06-25T01:18:46Z"}],"graph_snapshots":[{"event_id":"sha256:006706bfb24003f97ddcffa0307547809de4ded1e7a526175d37338663373083","target":"graph","created_at":"2026-06-25T01:18:46Z","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/2606.26038/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider weighted automata over the tropical semiring $\\mathbb{Z}_\\infty(min, +)$. Recently, it was shown that determinisation is decidable; in this paper we focus on the complexity when the alphabet is unary. In 2001, Lombardy showed this problem is decidable, a close inspection of his proof yields a coNP upper bound on the complexity. Earlier Gaubert showed that every weighted automaton in this setting can be effectively turned into an equivalent union of deterministic weighted automata. We prove Gaubert's result efficiently, presenting it as a generalisation of Chrobak's normal form for ","authors_text":"David Purser, Filip Mazowiecki, Henery Sinclair-Banks, Isma\\\"el Jecker, {\\L}ukasz Orlikowski, Shaull Almagor","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2026-06-24T17:13:53Z","title":"Representing One Letter Weighted Automata Over the Tropical Semiring"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.26038","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:d11b3b37d0a5a4917135af641246c9ca50666b79d85fbb1fcbbc6b90f1e5ccf3","target":"record","created_at":"2026-06-25T01:18:46Z","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":"9a165d73b977a834e3baace959fa1705fd7fdc07011e57c0fe1694fccf875e9e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2026-06-24T17:13:53Z","title_canon_sha256":"06791d82406cb68420c7468b6cad6ba7f0d02bb22b07638763539f01f3e90a65"},"schema_version":"1.0","source":{"id":"2606.26038","kind":"arxiv","version":1}},"canonical_sha256":"f21ecb24f60eb6930082af1e3e91a391ff0986569d0b49066910a1d04808b2c7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f21ecb24f60eb6930082af1e3e91a391ff0986569d0b49066910a1d04808b2c7","first_computed_at":"2026-06-25T01:18:46.539505Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-25T01:18:46.539505Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g0EcIjMReg/PvgsBX0odXsbUTWlZlhNPxtGDy/gVjtB4JVPqj1kAfZKQCUK7fd2v4SxYAUlt60QPHAlGQe5RBg==","signature_status":"signed_v1","signed_at":"2026-06-25T01:18:46.539863Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.26038","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d11b3b37d0a5a4917135af641246c9ca50666b79d85fbb1fcbbc6b90f1e5ccf3","sha256:006706bfb24003f97ddcffa0307547809de4ded1e7a526175d37338663373083"],"state_sha256":"034bd1ed6c006044f59fdd2869fab48ecd3ba5f9cef4337c314bed7af580aff7"}