{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:UG343VW3QSVCB2PYR3GRDTUS5J","short_pith_number":"pith:UG343VW3","canonical_record":{"source":{"id":"1511.06260","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-11-19T17:03:20Z","cross_cats_sorted":["cs.LO"],"title_canon_sha256":"8221b2c07cfb83c18d2d8e64827ef579cca6ef5ee1af4bbcf89d6837cf9f3281","abstract_canon_sha256":"da737dff91478033f3aeaeeb35a13c03511bcf8421d263b61a3bc6aa800e39ab"},"schema_version":"1.0"},"canonical_sha256":"a1b7cdd6db84aa20e9f88ecd11ce92ea59adb978458c65653357cb5c48c65502","source":{"kind":"arxiv","id":"1511.06260","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.06260","created_at":"2026-05-18T01:09:29Z"},{"alias_kind":"arxiv_version","alias_value":"1511.06260v3","created_at":"2026-05-18T01:09:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.06260","created_at":"2026-05-18T01:09:29Z"},{"alias_kind":"pith_short_12","alias_value":"UG343VW3QSVC","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UG343VW3QSVCB2PY","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UG343VW3","created_at":"2026-05-18T12:29:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:UG343VW3QSVCB2PYR3GRDTUS5J","target":"record","payload":{"canonical_record":{"source":{"id":"1511.06260","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-11-19T17:03:20Z","cross_cats_sorted":["cs.LO"],"title_canon_sha256":"8221b2c07cfb83c18d2d8e64827ef579cca6ef5ee1af4bbcf89d6837cf9f3281","abstract_canon_sha256":"da737dff91478033f3aeaeeb35a13c03511bcf8421d263b61a3bc6aa800e39ab"},"schema_version":"1.0"},"canonical_sha256":"a1b7cdd6db84aa20e9f88ecd11ce92ea59adb978458c65653357cb5c48c65502","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:29.657891Z","signature_b64":"F5AnmqeS0rGZiVSxG/SA5wQylhK7hxl0s01E2PTASHi0JY16WUT5i9HjQPZMaZT3LWEHEJ/BiYcYIkmk0Lj+Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a1b7cdd6db84aa20e9f88ecd11ce92ea59adb978458c65653357cb5c48c65502","last_reissued_at":"2026-05-18T01:09:29.657531Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:29.657531Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.06260","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:09:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E02y6RBL10mFx1PihULdZ3BrZ1o/DzZRonhSkvGSvxORhlqJDgOtLXoR5MiOUFf4IQKLe1rS6yE4dXxx2lIQDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T23:04:45.361946Z"},"content_sha256":"81637c456ae4f747066ac33c1b0f40a7e9d5279147f0bed8f22174f511c5d4f8","schema_version":"1.0","event_id":"sha256:81637c456ae4f747066ac33c1b0f40a7e9d5279147f0bed8f22174f511c5d4f8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:UG343VW3QSVCB2PYR3GRDTUS5J","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Game Semantics and the Geometry of Backtracking: a New Complexity Analysis of Interaction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"math.LO","authors_text":"Federico Aschieri","submitted_at":"2015-11-19T17:03:20Z","abstract_excerpt":"We present abstract complexity results about Coquand and Hyland-Ong game semantics, that will lead to new bounds on the length of first-order cut-elimination, normalization, interaction between expansion trees and any other dialogical process game semantics can model and apply to. In particular, we provide a novel method to bound the length of interactions between visible strategies and to measure precisely the tower of exponentials defining the worst-case complexity. Our study improves the old estimates on average by several exponentials."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.06260","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":""},"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":"2026-05-18T01:09:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bBWUgU0geqfWpinF5ogeEQy1pvFJ7zoA0BW3Qcslhi522P5t44QEjOnENU7dZz7lmaFFBHM4ne2IrOzoPUITBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T23:04:45.362283Z"},"content_sha256":"bb02afa61d109d02b8ca6c0a88200655614662707a80af5f1ef924b12724327c","schema_version":"1.0","event_id":"sha256:bb02afa61d109d02b8ca6c0a88200655614662707a80af5f1ef924b12724327c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UG343VW3QSVCB2PYR3GRDTUS5J/bundle.json","state_url":"https://pith.science/pith/UG343VW3QSVCB2PYR3GRDTUS5J/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UG343VW3QSVCB2PYR3GRDTUS5J/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":"2026-06-21T23:04:45Z","links":{"resolver":"https://pith.science/pith/UG343VW3QSVCB2PYR3GRDTUS5J","bundle":"https://pith.science/pith/UG343VW3QSVCB2PYR3GRDTUS5J/bundle.json","state":"https://pith.science/pith/UG343VW3QSVCB2PYR3GRDTUS5J/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UG343VW3QSVCB2PYR3GRDTUS5J/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:UG343VW3QSVCB2PYR3GRDTUS5J","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":"da737dff91478033f3aeaeeb35a13c03511bcf8421d263b61a3bc6aa800e39ab","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-11-19T17:03:20Z","title_canon_sha256":"8221b2c07cfb83c18d2d8e64827ef579cca6ef5ee1af4bbcf89d6837cf9f3281"},"schema_version":"1.0","source":{"id":"1511.06260","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.06260","created_at":"2026-05-18T01:09:29Z"},{"alias_kind":"arxiv_version","alias_value":"1511.06260v3","created_at":"2026-05-18T01:09:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.06260","created_at":"2026-05-18T01:09:29Z"},{"alias_kind":"pith_short_12","alias_value":"UG343VW3QSVC","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UG343VW3QSVCB2PY","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UG343VW3","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:bb02afa61d109d02b8ca6c0a88200655614662707a80af5f1ef924b12724327c","target":"graph","created_at":"2026-05-18T01:09:29Z","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 present abstract complexity results about Coquand and Hyland-Ong game semantics, that will lead to new bounds on the length of first-order cut-elimination, normalization, interaction between expansion trees and any other dialogical process game semantics can model and apply to. In particular, we provide a novel method to bound the length of interactions between visible strategies and to measure precisely the tower of exponentials defining the worst-case complexity. Our study improves the old estimates on average by several exponentials.","authors_text":"Federico Aschieri","cross_cats":["cs.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-11-19T17:03:20Z","title":"Game Semantics and the Geometry of Backtracking: a New Complexity Analysis of Interaction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.06260","kind":"arxiv","version":3},"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":"sha256:81637c456ae4f747066ac33c1b0f40a7e9d5279147f0bed8f22174f511c5d4f8","target":"record","created_at":"2026-05-18T01:09:29Z","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":"da737dff91478033f3aeaeeb35a13c03511bcf8421d263b61a3bc6aa800e39ab","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-11-19T17:03:20Z","title_canon_sha256":"8221b2c07cfb83c18d2d8e64827ef579cca6ef5ee1af4bbcf89d6837cf9f3281"},"schema_version":"1.0","source":{"id":"1511.06260","kind":"arxiv","version":3}},"canonical_sha256":"a1b7cdd6db84aa20e9f88ecd11ce92ea59adb978458c65653357cb5c48c65502","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a1b7cdd6db84aa20e9f88ecd11ce92ea59adb978458c65653357cb5c48c65502","first_computed_at":"2026-05-18T01:09:29.657531Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:29.657531Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F5AnmqeS0rGZiVSxG/SA5wQylhK7hxl0s01E2PTASHi0JY16WUT5i9HjQPZMaZT3LWEHEJ/BiYcYIkmk0Lj+Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:29.657891Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.06260","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:81637c456ae4f747066ac33c1b0f40a7e9d5279147f0bed8f22174f511c5d4f8","sha256:bb02afa61d109d02b8ca6c0a88200655614662707a80af5f1ef924b12724327c"],"state_sha256":"a026859facad15734b1d93c9bc15aa4cd22a0084dc3aa1cb393f45c49adda952"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lXGWjs+TR/DgsNOV42uS28Ncn2/w/XSDmiHaSDNuVHCwe9aJ6P7+VIAO+ulqiFCimFFkciL4gsiCMRByuzDSCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T23:04:45.364243Z","bundle_sha256":"f7386043e968e02f6ca0980f51cebcee0719a2d9cc3b8760b20b5a721f35cdc6"}}