{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:IRG6TQ6ACYBO4DNOXWP4C7C6NM","short_pith_number":"pith:IRG6TQ6A","schema_version":"1.0","canonical_sha256":"444de9c3c01602ee0daebd9fc17c5e6b20e61c999869be7ab55791e864b113f5","source":{"kind":"arxiv","id":"2601.19302","version":3},"attestation_state":"computed","paper":{"title":"Formula-One Prompting: A Composable Equation-First Prefix for Applied Mathematics","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.CL","authors_text":"Kunat Pipatanakul, Natapong Nitarach, Pittawat Taveekitworachai","submitted_at":"2026-01-27T07:42:20Z","abstract_excerpt":"This paper introduces Formula Prompting (FP) and Formula-One Prompting (F-1), two single-call methods that elicit governing equations before solving applied-math problems. Chain-of-Thought (CoT) and Program-of-Thought (PoT) prompting improve mathematical reasoning by eliciting reasoning traces or code-like structures learned during pretraining. This suggests a diagnostic question: which useful pretraining patterns remain under-elicited? Using infini-gram-mini, we scan 81.7 trillion pretraining tokens and find that, in curated corpora such as DataComp-LM, equation-centered language appears 121x"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2601.19302","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CL","submitted_at":"2026-01-27T07:42:20Z","cross_cats_sorted":[],"title_canon_sha256":"1d068254048910a3d7edee0b4f20a4585482eb73c5295affef8fda4bebc06ee9","abstract_canon_sha256":"d5f784097217b498002490509e168fccd78ccb0dbe72455d69ec11061b18e5ff"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-28T01:04:35.689482Z","signature_b64":"IPAPwwfjVkV3G8sDto5m7WJy1B74f8+qQXIcEqOCvrhJLoebAZBeMQwGq97J7+X5ndUCNl4Yt/956WdAPPwdDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"444de9c3c01602ee0daebd9fc17c5e6b20e61c999869be7ab55791e864b113f5","last_reissued_at":"2026-05-28T01:04:35.689024Z","signature_status":"signed_v1","first_computed_at":"2026-05-28T01:04:35.689024Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Formula-One Prompting: A Composable Equation-First Prefix for Applied Mathematics","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.CL","authors_text":"Kunat Pipatanakul, Natapong Nitarach, Pittawat Taveekitworachai","submitted_at":"2026-01-27T07:42:20Z","abstract_excerpt":"This paper introduces Formula Prompting (FP) and Formula-One Prompting (F-1), two single-call methods that elicit governing equations before solving applied-math problems. Chain-of-Thought (CoT) and Program-of-Thought (PoT) prompting improve mathematical reasoning by eliciting reasoning traces or code-like structures learned during pretraining. This suggests a diagnostic question: which useful pretraining patterns remain under-elicited? Using infini-gram-mini, we scan 81.7 trillion pretraining tokens and find that, in curated corpora such as DataComp-LM, equation-centered language appears 121x"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.19302","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/2601.19302/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2601.19302","created_at":"2026-05-28T01:04:35.689081+00:00"},{"alias_kind":"arxiv_version","alias_value":"2601.19302v3","created_at":"2026-05-28T01:04:35.689081+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2601.19302","created_at":"2026-05-28T01:04:35.689081+00:00"},{"alias_kind":"pith_short_12","alias_value":"IRG6TQ6ACYBO","created_at":"2026-05-28T01:04:35.689081+00:00"},{"alias_kind":"pith_short_16","alias_value":"IRG6TQ6ACYBO4DNO","created_at":"2026-05-28T01:04:35.689081+00:00"},{"alias_kind":"pith_short_8","alias_value":"IRG6TQ6A","created_at":"2026-05-28T01:04:35.689081+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/IRG6TQ6ACYBO4DNOXWP4C7C6NM","json":"https://pith.science/pith/IRG6TQ6ACYBO4DNOXWP4C7C6NM.json","graph_json":"https://pith.science/api/pith-number/IRG6TQ6ACYBO4DNOXWP4C7C6NM/graph.json","events_json":"https://pith.science/api/pith-number/IRG6TQ6ACYBO4DNOXWP4C7C6NM/events.json","paper":"https://pith.science/paper/IRG6TQ6A"},"agent_actions":{"view_html":"https://pith.science/pith/IRG6TQ6ACYBO4DNOXWP4C7C6NM","download_json":"https://pith.science/pith/IRG6TQ6ACYBO4DNOXWP4C7C6NM.json","view_paper":"https://pith.science/paper/IRG6TQ6A","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2601.19302&json=true","fetch_graph":"https://pith.science/api/pith-number/IRG6TQ6ACYBO4DNOXWP4C7C6NM/graph.json","fetch_events":"https://pith.science/api/pith-number/IRG6TQ6ACYBO4DNOXWP4C7C6NM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IRG6TQ6ACYBO4DNOXWP4C7C6NM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IRG6TQ6ACYBO4DNOXWP4C7C6NM/action/storage_attestation","attest_author":"https://pith.science/pith/IRG6TQ6ACYBO4DNOXWP4C7C6NM/action/author_attestation","sign_citation":"https://pith.science/pith/IRG6TQ6ACYBO4DNOXWP4C7C6NM/action/citation_signature","submit_replication":"https://pith.science/pith/IRG6TQ6ACYBO4DNOXWP4C7C6NM/action/replication_record"}},"created_at":"2026-05-28T01:04:35.689081+00:00","updated_at":"2026-05-28T01:04:35.689081+00:00"}