{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:HNWKYZH4A6KD2MWNPEZMDOLDG6","short_pith_number":"pith:HNWKYZH4","canonical_record":{"source":{"id":"1507.08056","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2015-07-29T08:21:41Z","cross_cats_sorted":[],"title_canon_sha256":"a39bd29cde0bf4916e22a1925fd3b1b7891959bcfa9db4462903eb73179776c7","abstract_canon_sha256":"5f4e4ed61f9f578bc3ffe87f6dc682fe941ad52feccf275454dda891d88f1904"},"schema_version":"1.0"},"canonical_sha256":"3b6cac64fc07943d32cd7932c1b96337835f7ed88e7f519189baba8e062789c4","source":{"kind":"arxiv","id":"1507.08056","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.08056","created_at":"2026-05-18T01:36:08Z"},{"alias_kind":"arxiv_version","alias_value":"1507.08056v1","created_at":"2026-05-18T01:36:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.08056","created_at":"2026-05-18T01:36:08Z"},{"alias_kind":"pith_short_12","alias_value":"HNWKYZH4A6KD","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HNWKYZH4A6KD2MWN","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HNWKYZH4","created_at":"2026-05-18T12:29:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:HNWKYZH4A6KD2MWNPEZMDOLDG6","target":"record","payload":{"canonical_record":{"source":{"id":"1507.08056","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2015-07-29T08:21:41Z","cross_cats_sorted":[],"title_canon_sha256":"a39bd29cde0bf4916e22a1925fd3b1b7891959bcfa9db4462903eb73179776c7","abstract_canon_sha256":"5f4e4ed61f9f578bc3ffe87f6dc682fe941ad52feccf275454dda891d88f1904"},"schema_version":"1.0"},"canonical_sha256":"3b6cac64fc07943d32cd7932c1b96337835f7ed88e7f519189baba8e062789c4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:08.450587Z","signature_b64":"soZwcD3Lvz8vTPL18ZSDmT9IPPh+8BeKzIveL7iSoonB/KdmHTX2mRpLkv89HDaSV1vKrHCryCvWwwU+D4mnBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b6cac64fc07943d32cd7932c1b96337835f7ed88e7f519189baba8e062789c4","last_reissued_at":"2026-05-18T01:36:08.449926Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:08.449926Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.08056","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":"2026-05-18T01:36:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k4w+G9xbltDTp7pkRal299s+S4/IEh5N4eNi/j0IBiFffhM0+HXgDn3g5R/oEjHq0KHHRua5DHuzpg85sjH7Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T07:07:20.458923Z"},"content_sha256":"5d4f8c1b08a4db4fa11ab9cd58594be6f029348def55bc00a39ad484f0f64c53","schema_version":"1.0","event_id":"sha256:5d4f8c1b08a4db4fa11ab9cd58594be6f029348def55bc00a39ad484f0f64c53"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:HNWKYZH4A6KD2MWNPEZMDOLDG6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sequent Calculus and Equational Programming","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Daniel Gustafsson (IT University of Copenhagen), Nicolas Guenot (IT University of Copenhagen)","submitted_at":"2015-07-29T08:21:41Z","abstract_excerpt":"Proof assistants and programming languages based on type theories usually come in two flavours: one is based on the standard natural deduction presentation of type theory and involves eliminators, while the other provides a syntax in equational style. We show here that the equational approach corresponds to the use of a focused presentation of a type theory expressed as a sequent calculus. A typed functional language is presented, based on a sequent calculus, that we relate to the syntax and internal language of Agda. In particular, we discuss the use of patterns and case splittings, as well a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.08056","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":""},"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":"2026-05-18T01:36:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+fk1vhlaurITW5F0f6YcvgNMAG4laSV/eVtH18eacZHY9NaIxjwRtO2PqQjUfbgpLj3TFTgYE5KStHnVxTEuDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T07:07:20.459475Z"},"content_sha256":"e0abe316dfd3c740098e5bf0fd6177ab27dbc9647a043ffd0333fd9f00fc9a78","schema_version":"1.0","event_id":"sha256:e0abe316dfd3c740098e5bf0fd6177ab27dbc9647a043ffd0333fd9f00fc9a78"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HNWKYZH4A6KD2MWNPEZMDOLDG6/bundle.json","state_url":"https://pith.science/pith/HNWKYZH4A6KD2MWNPEZMDOLDG6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HNWKYZH4A6KD2MWNPEZMDOLDG6/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":"2026-06-26T07:07:20Z","links":{"resolver":"https://pith.science/pith/HNWKYZH4A6KD2MWNPEZMDOLDG6","bundle":"https://pith.science/pith/HNWKYZH4A6KD2MWNPEZMDOLDG6/bundle.json","state":"https://pith.science/pith/HNWKYZH4A6KD2MWNPEZMDOLDG6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HNWKYZH4A6KD2MWNPEZMDOLDG6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:HNWKYZH4A6KD2MWNPEZMDOLDG6","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":"5f4e4ed61f9f578bc3ffe87f6dc682fe941ad52feccf275454dda891d88f1904","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2015-07-29T08:21:41Z","title_canon_sha256":"a39bd29cde0bf4916e22a1925fd3b1b7891959bcfa9db4462903eb73179776c7"},"schema_version":"1.0","source":{"id":"1507.08056","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.08056","created_at":"2026-05-18T01:36:08Z"},{"alias_kind":"arxiv_version","alias_value":"1507.08056v1","created_at":"2026-05-18T01:36:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.08056","created_at":"2026-05-18T01:36:08Z"},{"alias_kind":"pith_short_12","alias_value":"HNWKYZH4A6KD","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HNWKYZH4A6KD2MWN","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HNWKYZH4","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:e0abe316dfd3c740098e5bf0fd6177ab27dbc9647a043ffd0333fd9f00fc9a78","target":"graph","created_at":"2026-05-18T01:36:08Z","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"},"paper":{"abstract_excerpt":"Proof assistants and programming languages based on type theories usually come in two flavours: one is based on the standard natural deduction presentation of type theory and involves eliminators, while the other provides a syntax in equational style. We show here that the equational approach corresponds to the use of a focused presentation of a type theory expressed as a sequent calculus. A typed functional language is presented, based on a sequent calculus, that we relate to the syntax and internal language of Agda. In particular, we discuss the use of patterns and case splittings, as well a","authors_text":"Daniel Gustafsson (IT University of Copenhagen), Nicolas Guenot (IT University of Copenhagen)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2015-07-29T08:21:41Z","title":"Sequent Calculus and Equational Programming"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.08056","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":"sha256:5d4f8c1b08a4db4fa11ab9cd58594be6f029348def55bc00a39ad484f0f64c53","target":"record","created_at":"2026-05-18T01:36:08Z","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":"5f4e4ed61f9f578bc3ffe87f6dc682fe941ad52feccf275454dda891d88f1904","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2015-07-29T08:21:41Z","title_canon_sha256":"a39bd29cde0bf4916e22a1925fd3b1b7891959bcfa9db4462903eb73179776c7"},"schema_version":"1.0","source":{"id":"1507.08056","kind":"arxiv","version":1}},"canonical_sha256":"3b6cac64fc07943d32cd7932c1b96337835f7ed88e7f519189baba8e062789c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b6cac64fc07943d32cd7932c1b96337835f7ed88e7f519189baba8e062789c4","first_computed_at":"2026-05-18T01:36:08.449926Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:08.449926Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"soZwcD3Lvz8vTPL18ZSDmT9IPPh+8BeKzIveL7iSoonB/KdmHTX2mRpLkv89HDaSV1vKrHCryCvWwwU+D4mnBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:08.450587Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.08056","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d4f8c1b08a4db4fa11ab9cd58594be6f029348def55bc00a39ad484f0f64c53","sha256:e0abe316dfd3c740098e5bf0fd6177ab27dbc9647a043ffd0333fd9f00fc9a78"],"state_sha256":"b351722c2b7001b2233d4838b41c501202d528680ca3ec09e5319621be91ffc0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RRKqscqQBrVWTVCmt4RM79kiKB700yHFPe2QhyAJnfBRWFtAxPQj+/3bbh4ww0yM67OJIMELtDRsosHW6qW0CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T07:07:20.461875Z","bundle_sha256":"1bb581ea6ce22851b6353119b8a693de1da6d842628d3594276702b751d29b81"}}