{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:6QXIB2TABOSH4JGRMKRFIQS4EH","short_pith_number":"pith:6QXIB2TA","canonical_record":{"source":{"id":"1103.0510","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.PL","submitted_at":"2011-03-02T18:21:59Z","cross_cats_sorted":["cs.LO"],"title_canon_sha256":"01e2e1f147535d503749883ff5013ff8d6c0c15b4c6de7ceac45ac1033571a05","abstract_canon_sha256":"00e71030e75d6c5b6fcff11b2cef8fcca1df36a80c0ad24357a7874e81dfa97a"},"schema_version":"1.0"},"canonical_sha256":"f42e80ea600ba47e24d162a254425c21e18b16ce093bdf3c9a7b07f5ac1ff138","source":{"kind":"arxiv","id":"1103.0510","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.0510","created_at":"2026-05-18T01:37:39Z"},{"alias_kind":"arxiv_version","alias_value":"1103.0510v2","created_at":"2026-05-18T01:37:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.0510","created_at":"2026-05-18T01:37:39Z"},{"alias_kind":"pith_short_12","alias_value":"6QXIB2TABOSH","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"6QXIB2TABOSH4JGR","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"6QXIB2TA","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:6QXIB2TABOSH4JGRMKRFIQS4EH","target":"record","payload":{"canonical_record":{"source":{"id":"1103.0510","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.PL","submitted_at":"2011-03-02T18:21:59Z","cross_cats_sorted":["cs.LO"],"title_canon_sha256":"01e2e1f147535d503749883ff5013ff8d6c0c15b4c6de7ceac45ac1033571a05","abstract_canon_sha256":"00e71030e75d6c5b6fcff11b2cef8fcca1df36a80c0ad24357a7874e81dfa97a"},"schema_version":"1.0"},"canonical_sha256":"f42e80ea600ba47e24d162a254425c21e18b16ce093bdf3c9a7b07f5ac1ff138","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:39.611416Z","signature_b64":"5aL1j+cQshx1mhbdJ0guK/+VnVjblm9QbHHxL6BKMDsTz11UxfuWnQeb3M86/6JrE+m96CwSF3criuE/lsZYDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f42e80ea600ba47e24d162a254425c21e18b16ce093bdf3c9a7b07f5ac1ff138","last_reissued_at":"2026-05-18T01:37:39.610758Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:39.610758Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1103.0510","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:37:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c4cakdkyle5cpKZ0DaOc4IS+2zWMw6cfTsXl0lUgbfG3SYPQKK0IACKObn6G2Qfppf8UKB/kZhIxVLwYfKu3Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T14:07:14.347388Z"},"content_sha256":"e23f2c787b6a66ce6075cb35ff69e5868538b7b09af4c70edd78791eb6c34b14","schema_version":"1.0","event_id":"sha256:e23f2c787b6a66ce6075cb35ff69e5868538b7b09af4c70edd78791eb6c34b14"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:6QXIB2TABOSH4JGRMKRFIQS4EH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Logical Step-Indexed Logical Relations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"cs.PL","authors_text":"Amal Ahmed (Indiana University), Derek Dreyer (MPI-SWS), Lars Birkedal (IT University of Copenhagen)","submitted_at":"2011-03-02T18:21:59Z","abstract_excerpt":"Appel and McAllester's \"step-indexed\" logical relations have proven to be a simple and effective technique for reasoning about programs in languages with semantically interesting types, such as general recursive types and general reference types. However, proofs using step-indexed models typically involve tedious, error-prone, and proof-obscuring step-index arithmetic, so it is important to develop clean, high-level, equational proof principles that avoid mention of step indices. In this paper, we show how to reason about binary step-indexed logical relations in an abstract and elegant way. Sp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.0510","kind":"arxiv","version":2},"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":"2026-05-18T01:37:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9ekCt7LFJ/jTtl6Q6408GcU0gLwgSZ6C+zsWW4Xet8ko3WnDLsFoTbdZn4dyx7IfdpOqXI7DbR/IgRIauLZyAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T14:07:14.347747Z"},"content_sha256":"dedb9f1c42a01e1e57576661fe2104072bdc2ab6c6d3924ea88c8103170353b5","schema_version":"1.0","event_id":"sha256:dedb9f1c42a01e1e57576661fe2104072bdc2ab6c6d3924ea88c8103170353b5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6QXIB2TABOSH4JGRMKRFIQS4EH/bundle.json","state_url":"https://pith.science/pith/6QXIB2TABOSH4JGRMKRFIQS4EH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6QXIB2TABOSH4JGRMKRFIQS4EH/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":"2026-06-01T14:07:14Z","links":{"resolver":"https://pith.science/pith/6QXIB2TABOSH4JGRMKRFIQS4EH","bundle":"https://pith.science/pith/6QXIB2TABOSH4JGRMKRFIQS4EH/bundle.json","state":"https://pith.science/pith/6QXIB2TABOSH4JGRMKRFIQS4EH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6QXIB2TABOSH4JGRMKRFIQS4EH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:6QXIB2TABOSH4JGRMKRFIQS4EH","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":"00e71030e75d6c5b6fcff11b2cef8fcca1df36a80c0ad24357a7874e81dfa97a","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.PL","submitted_at":"2011-03-02T18:21:59Z","title_canon_sha256":"01e2e1f147535d503749883ff5013ff8d6c0c15b4c6de7ceac45ac1033571a05"},"schema_version":"1.0","source":{"id":"1103.0510","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.0510","created_at":"2026-05-18T01:37:39Z"},{"alias_kind":"arxiv_version","alias_value":"1103.0510v2","created_at":"2026-05-18T01:37:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.0510","created_at":"2026-05-18T01:37:39Z"},{"alias_kind":"pith_short_12","alias_value":"6QXIB2TABOSH","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"6QXIB2TABOSH4JGR","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"6QXIB2TA","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:dedb9f1c42a01e1e57576661fe2104072bdc2ab6c6d3924ea88c8103170353b5","target":"graph","created_at":"2026-05-18T01:37:39Z","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":"Appel and McAllester's \"step-indexed\" logical relations have proven to be a simple and effective technique for reasoning about programs in languages with semantically interesting types, such as general recursive types and general reference types. However, proofs using step-indexed models typically involve tedious, error-prone, and proof-obscuring step-index arithmetic, so it is important to develop clean, high-level, equational proof principles that avoid mention of step indices. In this paper, we show how to reason about binary step-indexed logical relations in an abstract and elegant way. Sp","authors_text":"Amal Ahmed (Indiana University), Derek Dreyer (MPI-SWS), Lars Birkedal (IT University of Copenhagen)","cross_cats":["cs.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.PL","submitted_at":"2011-03-02T18:21:59Z","title":"Logical Step-Indexed Logical Relations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.0510","kind":"arxiv","version":2},"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:e23f2c787b6a66ce6075cb35ff69e5868538b7b09af4c70edd78791eb6c34b14","target":"record","created_at":"2026-05-18T01:37:39Z","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":"00e71030e75d6c5b6fcff11b2cef8fcca1df36a80c0ad24357a7874e81dfa97a","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.PL","submitted_at":"2011-03-02T18:21:59Z","title_canon_sha256":"01e2e1f147535d503749883ff5013ff8d6c0c15b4c6de7ceac45ac1033571a05"},"schema_version":"1.0","source":{"id":"1103.0510","kind":"arxiv","version":2}},"canonical_sha256":"f42e80ea600ba47e24d162a254425c21e18b16ce093bdf3c9a7b07f5ac1ff138","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f42e80ea600ba47e24d162a254425c21e18b16ce093bdf3c9a7b07f5ac1ff138","first_computed_at":"2026-05-18T01:37:39.610758Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:39.610758Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5aL1j+cQshx1mhbdJ0guK/+VnVjblm9QbHHxL6BKMDsTz11UxfuWnQeb3M86/6JrE+m96CwSF3criuE/lsZYDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:39.611416Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.0510","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e23f2c787b6a66ce6075cb35ff69e5868538b7b09af4c70edd78791eb6c34b14","sha256:dedb9f1c42a01e1e57576661fe2104072bdc2ab6c6d3924ea88c8103170353b5"],"state_sha256":"791fa38ce87cfcca99974a37e165efe93f0e2cedd7f2aebb1a15ba837db6f9dd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F4HCjXm9yUnkBTWbAZytkTnI0F7krw0o+4jU1T5EmgvwPGzGbK7OXkvWb+38q7mdFeSRvuqGFQsvJ3F8Olr2DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T14:07:14.349838Z","bundle_sha256":"6c1b872287f4d40de31822876f2a68b0c6e420d87a85a55dffb1148f9ca8691a"}}