{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:PTNVCDJK5OY6U62J5EME52ZQBP","short_pith_number":"pith:PTNVCDJK","canonical_record":{"source":{"id":"1210.6857","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2012-10-25T14:40:48Z","cross_cats_sorted":["cs.PL"],"title_canon_sha256":"0891d13d632e28ef30af2097d435409f2e45d529a75bde10ff6e69b624db980a","abstract_canon_sha256":"5e451049c8b0e42a5155adbc10435f91e15e0a7064a957637f7a43c21274990f"},"schema_version":"1.0"},"canonical_sha256":"7cdb510d2aebb1ea7b49e9184eeb300bf31b1b5a26d4fe49983359f0a61074e9","source":{"kind":"arxiv","id":"1210.6857","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.6857","created_at":"2026-05-18T03:42:22Z"},{"alias_kind":"arxiv_version","alias_value":"1210.6857v1","created_at":"2026-05-18T03:42:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.6857","created_at":"2026-05-18T03:42:22Z"},{"alias_kind":"pith_short_12","alias_value":"PTNVCDJK5OY6","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PTNVCDJK5OY6U62J","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PTNVCDJK","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:PTNVCDJK5OY6U62J5EME52ZQBP","target":"record","payload":{"canonical_record":{"source":{"id":"1210.6857","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2012-10-25T14:40:48Z","cross_cats_sorted":["cs.PL"],"title_canon_sha256":"0891d13d632e28ef30af2097d435409f2e45d529a75bde10ff6e69b624db980a","abstract_canon_sha256":"5e451049c8b0e42a5155adbc10435f91e15e0a7064a957637f7a43c21274990f"},"schema_version":"1.0"},"canonical_sha256":"7cdb510d2aebb1ea7b49e9184eeb300bf31b1b5a26d4fe49983359f0a61074e9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:42:22.967209Z","signature_b64":"u187F/8+k1wdUksDfoyFOFwi1Qf0njFzo8k0jHn13YvYeuiLPvU8YhIszdlIGPcOtM/hhSLVM9S3kRGo8iVWAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7cdb510d2aebb1ea7b49e9184eeb300bf31b1b5a26d4fe49983359f0a61074e9","last_reissued_at":"2026-05-18T03:42:22.966588Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:42:22.966588Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.6857","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":"2026-05-18T03:42:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"avWwyyRR/nKS+yAvuX5YE1SXcs1eiqo3LPL2b8FYKAM5CK0ifO25zKcl+YgcueNmLdbfZUid6xJ6bCCu3JEbDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T05:50:59.776388Z"},"content_sha256":"9198fd8bebe90bc8e5db2a1620db651c03ec9be213a848c00e829333453fd636","schema_version":"1.0","event_id":"sha256:9198fd8bebe90bc8e5db2a1620db651c03ec9be213a848c00e829333453fd636"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:PTNVCDJK5OY6U62J5EME52ZQBP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Geometry of Types (Long Version)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.PL"],"primary_cat":"cs.LO","authors_text":"Barbara Petit, Ugo Dal Lago","submitted_at":"2012-10-25T14:40:48Z","abstract_excerpt":"We show that time complexity analysis of higher-order functional programs can be effectively reduced to an arguably simpler (although computationally equivalent) verification problem, namely checking first-order inequalities for validity. This is done by giving an efficient inference algorithm for linear dependent types which, given a PCF term, produces in output both a linear dependent type and a cost expression for the term, together with a set of proof obligations. Actually, the output type judgement is derivable iff all proof obligations are valid. This, coupled with the already known rela"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.6857","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":"2026-05-18T03:42:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"93gPtRaPnvU+KRPRm/AMDJEfSHNHH/l5ysZ70SGCKlvGAnl6bQVK1/SabVpUjNgfAIRhbfHtBrzCNwMqH0gHDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T05:50:59.776937Z"},"content_sha256":"8e522f6aa2470b7e6ba0a40e600d22a2a3c8b31ea89d99cf5d44721303bef6a9","schema_version":"1.0","event_id":"sha256:8e522f6aa2470b7e6ba0a40e600d22a2a3c8b31ea89d99cf5d44721303bef6a9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PTNVCDJK5OY6U62J5EME52ZQBP/bundle.json","state_url":"https://pith.science/pith/PTNVCDJK5OY6U62J5EME52ZQBP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PTNVCDJK5OY6U62J5EME52ZQBP/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":"2026-06-05T05:50:59Z","links":{"resolver":"https://pith.science/pith/PTNVCDJK5OY6U62J5EME52ZQBP","bundle":"https://pith.science/pith/PTNVCDJK5OY6U62J5EME52ZQBP/bundle.json","state":"https://pith.science/pith/PTNVCDJK5OY6U62J5EME52ZQBP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PTNVCDJK5OY6U62J5EME52ZQBP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:PTNVCDJK5OY6U62J5EME52ZQBP","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":"5e451049c8b0e42a5155adbc10435f91e15e0a7064a957637f7a43c21274990f","cross_cats_sorted":["cs.PL"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2012-10-25T14:40:48Z","title_canon_sha256":"0891d13d632e28ef30af2097d435409f2e45d529a75bde10ff6e69b624db980a"},"schema_version":"1.0","source":{"id":"1210.6857","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.6857","created_at":"2026-05-18T03:42:22Z"},{"alias_kind":"arxiv_version","alias_value":"1210.6857v1","created_at":"2026-05-18T03:42:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.6857","created_at":"2026-05-18T03:42:22Z"},{"alias_kind":"pith_short_12","alias_value":"PTNVCDJK5OY6","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PTNVCDJK5OY6U62J","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PTNVCDJK","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:8e522f6aa2470b7e6ba0a40e600d22a2a3c8b31ea89d99cf5d44721303bef6a9","target":"graph","created_at":"2026-05-18T03:42:22Z","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":"We show that time complexity analysis of higher-order functional programs can be effectively reduced to an arguably simpler (although computationally equivalent) verification problem, namely checking first-order inequalities for validity. This is done by giving an efficient inference algorithm for linear dependent types which, given a PCF term, produces in output both a linear dependent type and a cost expression for the term, together with a set of proof obligations. Actually, the output type judgement is derivable iff all proof obligations are valid. This, coupled with the already known rela","authors_text":"Barbara Petit, Ugo Dal Lago","cross_cats":["cs.PL"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2012-10-25T14:40:48Z","title":"The Geometry of Types (Long Version)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.6857","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":"sha256:9198fd8bebe90bc8e5db2a1620db651c03ec9be213a848c00e829333453fd636","target":"record","created_at":"2026-05-18T03:42:22Z","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":"5e451049c8b0e42a5155adbc10435f91e15e0a7064a957637f7a43c21274990f","cross_cats_sorted":["cs.PL"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2012-10-25T14:40:48Z","title_canon_sha256":"0891d13d632e28ef30af2097d435409f2e45d529a75bde10ff6e69b624db980a"},"schema_version":"1.0","source":{"id":"1210.6857","kind":"arxiv","version":1}},"canonical_sha256":"7cdb510d2aebb1ea7b49e9184eeb300bf31b1b5a26d4fe49983359f0a61074e9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7cdb510d2aebb1ea7b49e9184eeb300bf31b1b5a26d4fe49983359f0a61074e9","first_computed_at":"2026-05-18T03:42:22.966588Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:42:22.966588Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u187F/8+k1wdUksDfoyFOFwi1Qf0njFzo8k0jHn13YvYeuiLPvU8YhIszdlIGPcOtM/hhSLVM9S3kRGo8iVWAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:42:22.967209Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.6857","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9198fd8bebe90bc8e5db2a1620db651c03ec9be213a848c00e829333453fd636","sha256:8e522f6aa2470b7e6ba0a40e600d22a2a3c8b31ea89d99cf5d44721303bef6a9"],"state_sha256":"9b8798a8e4eec474cd1e53930324c75b208ea0e9d24fb865bac783740a5cc345"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4U7HBnVt1Rc2U0+BFd897XgElJNYK5DJFt4s6tkAklqENfjQYgXhfQj/gKZgLK7K+kXL+Dru5kbAlgnhqJB0Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T05:50:59.779591Z","bundle_sha256":"9f9d2d0fee9e6101d5555e413b2a39dcce372b3ad4fb6c096e7de25232c4599f"}}