{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:3LHKBYOPJZJZBPBSCTAKVVTHDW","short_pith_number":"pith:3LHKBYOP","canonical_record":{"source":{"id":"1005.2907","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2010-05-17T12:39:44Z","cross_cats_sorted":[],"title_canon_sha256":"94a53eb51c277ce64c111ada2052aa98d0c80847a056eefb7b01b651434cf01e","abstract_canon_sha256":"134716d19bba58d394fef8affd8e125333d8f44543703414f58f730ee095c070"},"schema_version":"1.0"},"canonical_sha256":"dacea0e1cf4e5390bc3214c0aad6671dbe8e1f92b666f4a11e4bde24a36e825b","source":{"kind":"arxiv","id":"1005.2907","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.2907","created_at":"2026-05-18T02:23:59Z"},{"alias_kind":"arxiv_version","alias_value":"1005.2907v1","created_at":"2026-05-18T02:23:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.2907","created_at":"2026-05-18T02:23:59Z"},{"alias_kind":"pith_short_12","alias_value":"3LHKBYOPJZJZ","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"3LHKBYOPJZJZBPBS","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"3LHKBYOP","created_at":"2026-05-18T12:26:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:3LHKBYOPJZJZBPBSCTAKVVTHDW","target":"record","payload":{"canonical_record":{"source":{"id":"1005.2907","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2010-05-17T12:39:44Z","cross_cats_sorted":[],"title_canon_sha256":"94a53eb51c277ce64c111ada2052aa98d0c80847a056eefb7b01b651434cf01e","abstract_canon_sha256":"134716d19bba58d394fef8affd8e125333d8f44543703414f58f730ee095c070"},"schema_version":"1.0"},"canonical_sha256":"dacea0e1cf4e5390bc3214c0aad6671dbe8e1f92b666f4a11e4bde24a36e825b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:23:59.272415Z","signature_b64":"K0Q8g5oj7uGpWgzP8brdjOuQY20XNt5yGCox/63Euz754q1xFalppdLQwlcEFYZKqLPa0r52AuZLV5DvT7ICAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dacea0e1cf4e5390bc3214c0aad6671dbe8e1f92b666f4a11e4bde24a36e825b","last_reissued_at":"2026-05-18T02:23:59.271702Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:23:59.271702Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1005.2907","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":"2026-05-18T02:23:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IikTU1Unim+6E+c4/UYsD8YFfiWYaCwbA5Z3gTumcYkaOSIwZicsHJx7MbPwHiuJ17eTGjkyPKRC02YFkl1SBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T01:54:56.447030Z"},"content_sha256":"7c6063cd9a340fceaad986055678ec5e88a275468703186368fb98006f3b4703","schema_version":"1.0","event_id":"sha256:7c6063cd9a340fceaad986055678ec5e88a275468703186368fb98006f3b4703"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:3LHKBYOPJZJZBPBSCTAKVVTHDW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Interactive Realizers and Monads","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Stefano Berardi, Ugo de'Liguoro","submitted_at":"2010-05-17T12:39:44Z","abstract_excerpt":"We propose a realizability interpretation of a system for quantifier free arithmetic which is equivalent to the fragment of classical arithmetic without \"nested\" quantifiers, called here EM1-arithmetic. We interpret classical proofs as interactive learning strategies, namely as processes going through several stages of knowledge and learning by interacting with the \"environment\" and with each other. We give a categorical presentation of the interpretation through the construction of two suitable monads."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.2907","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":"2026-05-18T02:23:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mu3n0GU+K+Fari0J80ijohzijt41K67EQN3K96ZamIQRS1m8T6yViw5qVxjMg49amwNjhdkrMQcidVU1z2S4Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T01:54:56.447376Z"},"content_sha256":"c624ad891bfb520aefc7fee0019e4fd9b69613a31a03884045ee5dc49735a8fb","schema_version":"1.0","event_id":"sha256:c624ad891bfb520aefc7fee0019e4fd9b69613a31a03884045ee5dc49735a8fb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3LHKBYOPJZJZBPBSCTAKVVTHDW/bundle.json","state_url":"https://pith.science/pith/3LHKBYOPJZJZBPBSCTAKVVTHDW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3LHKBYOPJZJZBPBSCTAKVVTHDW/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":"2026-05-31T01:54:56Z","links":{"resolver":"https://pith.science/pith/3LHKBYOPJZJZBPBSCTAKVVTHDW","bundle":"https://pith.science/pith/3LHKBYOPJZJZBPBSCTAKVVTHDW/bundle.json","state":"https://pith.science/pith/3LHKBYOPJZJZBPBSCTAKVVTHDW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3LHKBYOPJZJZBPBSCTAKVVTHDW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:3LHKBYOPJZJZBPBSCTAKVVTHDW","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":"134716d19bba58d394fef8affd8e125333d8f44543703414f58f730ee095c070","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2010-05-17T12:39:44Z","title_canon_sha256":"94a53eb51c277ce64c111ada2052aa98d0c80847a056eefb7b01b651434cf01e"},"schema_version":"1.0","source":{"id":"1005.2907","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.2907","created_at":"2026-05-18T02:23:59Z"},{"alias_kind":"arxiv_version","alias_value":"1005.2907v1","created_at":"2026-05-18T02:23:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.2907","created_at":"2026-05-18T02:23:59Z"},{"alias_kind":"pith_short_12","alias_value":"3LHKBYOPJZJZ","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"3LHKBYOPJZJZBPBS","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"3LHKBYOP","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:c624ad891bfb520aefc7fee0019e4fd9b69613a31a03884045ee5dc49735a8fb","target":"graph","created_at":"2026-05-18T02:23:59Z","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 propose a realizability interpretation of a system for quantifier free arithmetic which is equivalent to the fragment of classical arithmetic without \"nested\" quantifiers, called here EM1-arithmetic. We interpret classical proofs as interactive learning strategies, namely as processes going through several stages of knowledge and learning by interacting with the \"environment\" and with each other. We give a categorical presentation of the interpretation through the construction of two suitable monads.","authors_text":"Stefano Berardi, Ugo de'Liguoro","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2010-05-17T12:39:44Z","title":"Interactive Realizers and Monads"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.2907","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":"sha256:7c6063cd9a340fceaad986055678ec5e88a275468703186368fb98006f3b4703","target":"record","created_at":"2026-05-18T02:23:59Z","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":"134716d19bba58d394fef8affd8e125333d8f44543703414f58f730ee095c070","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2010-05-17T12:39:44Z","title_canon_sha256":"94a53eb51c277ce64c111ada2052aa98d0c80847a056eefb7b01b651434cf01e"},"schema_version":"1.0","source":{"id":"1005.2907","kind":"arxiv","version":1}},"canonical_sha256":"dacea0e1cf4e5390bc3214c0aad6671dbe8e1f92b666f4a11e4bde24a36e825b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dacea0e1cf4e5390bc3214c0aad6671dbe8e1f92b666f4a11e4bde24a36e825b","first_computed_at":"2026-05-18T02:23:59.271702Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:23:59.271702Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K0Q8g5oj7uGpWgzP8brdjOuQY20XNt5yGCox/63Euz754q1xFalppdLQwlcEFYZKqLPa0r52AuZLV5DvT7ICAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:23:59.272415Z","signed_message":"canonical_sha256_bytes"},"source_id":"1005.2907","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7c6063cd9a340fceaad986055678ec5e88a275468703186368fb98006f3b4703","sha256:c624ad891bfb520aefc7fee0019e4fd9b69613a31a03884045ee5dc49735a8fb"],"state_sha256":"07b177b1acb0c54a8a59ee508faf318f080071d5a3d41f4a5e17c8fbc17dd3d8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KvxDc+5tj5qO3jN/JEndHVcR3t0h9fNZiQ5ZrGYmZ5whlNg/HdcJAs4yLB3zd+ljrwOCw5q4Lz3Up9R/Z715Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T01:54:56.449293Z","bundle_sha256":"395cdf782b98334ec3854b4124f2fa627ecad17d5b64a70e32ada060fe303048"}}