{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:FUOTHTWTLB4ZLDKLE6UEACP2O6","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":"fd5b63afc9ede688d4a29f35989ac50b0db2cd0354607f2dd10c4c802a085805","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2026-07-02T08:15:49Z","title_canon_sha256":"c7e16c5f4a5adc7ef744535735eaa6485cb0467f5aea4752a97c98ff91a998b8"},"schema_version":"1.0","source":{"id":"2607.01856","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.01856","created_at":"2026-07-03T01:17:31Z"},{"alias_kind":"arxiv_version","alias_value":"2607.01856v1","created_at":"2026-07-03T01:17:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.01856","created_at":"2026-07-03T01:17:31Z"},{"alias_kind":"pith_short_12","alias_value":"FUOTHTWTLB4Z","created_at":"2026-07-03T01:17:31Z"},{"alias_kind":"pith_short_16","alias_value":"FUOTHTWTLB4ZLDKL","created_at":"2026-07-03T01:17:31Z"},{"alias_kind":"pith_short_8","alias_value":"FUOTHTWT","created_at":"2026-07-03T01:17:31Z"}],"graph_snapshots":[{"event_id":"sha256:c4f2dd7bc0ac8dfd18a0ce1e3a094766a995f94060219c0ce6f8cd27622fa314","target":"graph","created_at":"2026-07-03T01:17:31Z","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/2607.01856/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present an algebraic method for analyzing probabilistic programs with counters and discrete states, Generalized Constant Probability (GCP) programs. We define the operational semantics of GCP in terms of the runs of a type of probabilistic pushdown automata (pPDAs). We characterize the resulting (sub-)probability generating function (pgf) $\\Delta(z)$ as an algebraic function, representable via the roots of a kernel polynomial associated with the program. Next, we provide algorithms that, leveraging this information, compute under mild algebraic conditions the dominant singularities and the ","authors_text":"Alessandro Pompa Di Gregorio, Luisa Collodi, Michele Boreale","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2026-07-02T08:15:49Z","title":"On the algebraic analysis of runtime distribution of probabilistic programs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.01856","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:defe3e23a03d9f19984f03495be7c3a3f0d6cfb8afdadb214b34afe1c9474849","target":"record","created_at":"2026-07-03T01:17:31Z","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":"fd5b63afc9ede688d4a29f35989ac50b0db2cd0354607f2dd10c4c802a085805","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2026-07-02T08:15:49Z","title_canon_sha256":"c7e16c5f4a5adc7ef744535735eaa6485cb0467f5aea4752a97c98ff91a998b8"},"schema_version":"1.0","source":{"id":"2607.01856","kind":"arxiv","version":1}},"canonical_sha256":"2d1d33ced35879958d4b27a84009fa7795b89f38dec7910460adfa00a4af36d9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2d1d33ced35879958d4b27a84009fa7795b89f38dec7910460adfa00a4af36d9","first_computed_at":"2026-07-03T01:17:31.770912Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-03T01:17:31.770912Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dCUqdAyMq2u7oXS03vVuHDaxGgz6wd+aa/QS6UR/0KYfQV01bj9k0QyMPtkouOfElr2B+ErMsdFZkl60W+o6DA==","signature_status":"signed_v1","signed_at":"2026-07-03T01:17:31.771257Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.01856","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:defe3e23a03d9f19984f03495be7c3a3f0d6cfb8afdadb214b34afe1c9474849","sha256:c4f2dd7bc0ac8dfd18a0ce1e3a094766a995f94060219c0ce6f8cd27622fa314"],"state_sha256":"167e493666c4cc1c66c84c0ce7c88abc2ea5fc6c82823deb8e7291d9b4bd3926"}