{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:5TM6E7JCBYI2JV3K5IHE5ZKO52","short_pith_number":"pith:5TM6E7JC","canonical_record":{"source":{"id":"2506.05837","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2025-06-06T07:58:37Z","cross_cats_sorted":[],"title_canon_sha256":"d860fba7c5c1a1d979b6adbe2e4b2f322d7fbcc6874f0882be8ba3887be8e81d","abstract_canon_sha256":"a285d56ad0f6b878cba8bc3ae678fea5110d3bc2ae5409018b30ff4ec84a86da"},"schema_version":"1.0"},"canonical_sha256":"ecd9e27d220e11a4d76aea0e4ee54eeebb4ede72df391a9e9a723339b6c2726e","source":{"kind":"arxiv","id":"2506.05837","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.05837","created_at":"2026-07-05T11:17:10Z"},{"alias_kind":"arxiv_version","alias_value":"2506.05837v1","created_at":"2026-07-05T11:17:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.05837","created_at":"2026-07-05T11:17:10Z"},{"alias_kind":"pith_short_12","alias_value":"5TM6E7JCBYI2","created_at":"2026-07-05T11:17:10Z"},{"alias_kind":"pith_short_16","alias_value":"5TM6E7JCBYI2JV3K","created_at":"2026-07-05T11:17:10Z"},{"alias_kind":"pith_short_8","alias_value":"5TM6E7JC","created_at":"2026-07-05T11:17:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:5TM6E7JCBYI2JV3K5IHE5ZKO52","target":"record","payload":{"canonical_record":{"source":{"id":"2506.05837","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2025-06-06T07:58:37Z","cross_cats_sorted":[],"title_canon_sha256":"d860fba7c5c1a1d979b6adbe2e4b2f322d7fbcc6874f0882be8ba3887be8e81d","abstract_canon_sha256":"a285d56ad0f6b878cba8bc3ae678fea5110d3bc2ae5409018b30ff4ec84a86da"},"schema_version":"1.0"},"canonical_sha256":"ecd9e27d220e11a4d76aea0e4ee54eeebb4ede72df391a9e9a723339b6c2726e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:17:10.996421Z","signature_b64":"giWbg/hSE7w2j2N/RXHQCbLZzGhc1mqAoJ4NgIqoVDeq/JaCxXD/GTuQLW4v3UxVYo9Ms32SCABl8yISAe+TAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ecd9e27d220e11a4d76aea0e4ee54eeebb4ede72df391a9e9a723339b6c2726e","last_reissued_at":"2026-07-05T11:17:10.995934Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:17:10.995934Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.05837","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":"2026-07-05T11:17:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u1fPbrXzxICyoiTUMNXJrm3HnUCs6fX7Ax1M3Cdfk4rsXdCy+hv2w22FgjF9tsjeqOcVulJuw6TLiMLlNaGQCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T01:40:59.073280Z"},"content_sha256":"daf56fb3655f84d7f110324fee03bb762f53123a4a1bae095d2fa5310a5f8463","schema_version":"1.0","event_id":"sha256:daf56fb3655f84d7f110324fee03bb762f53123a4a1bae095d2fa5310a5f8463"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:5TM6E7JCBYI2JV3K5IHE5ZKO52","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Towards an Analysis of Proofs in Arithmetic","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Alexander Leitsch, Anela Loli\\'c, Stella Mahler","submitted_at":"2025-06-06T07:58:37Z","abstract_excerpt":"Inductive proofs can be represented as proof schemata, i.e. as parameterized sequences of proofs defined in a primitive recursive way. Applications of proof schemata can be found in the area of automated proof analysis where the schemata admit (schematic) cut-elimination and the construction of Herbrand systems. This work focuses on the expressivity of proof schemata. We show that proof schemata can simulate primitive recursive arithmetic. The translation of proofs in arithmetic to proof schemata can be considered as a crucial step in the analysis of inductive proofs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.05837","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.05837/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T11:17:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SQFFA+fIF3wWiIcaG/5eFXemKWEgP1yN99THg+ZwoGU3FEVmTpJOa1ivza9uVtuJc8ApyH8gEjVAnR84aolDDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T01:40:59.073872Z"},"content_sha256":"182e23517fe7ee415117e03e52023e534a5bd52fd28ea68c28b8c6bcc061d527","schema_version":"1.0","event_id":"sha256:182e23517fe7ee415117e03e52023e534a5bd52fd28ea68c28b8c6bcc061d527"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5TM6E7JCBYI2JV3K5IHE5ZKO52/bundle.json","state_url":"https://pith.science/pith/5TM6E7JCBYI2JV3K5IHE5ZKO52/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5TM6E7JCBYI2JV3K5IHE5ZKO52/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":"2026-08-09T01:40:59Z","links":{"resolver":"https://pith.science/pith/5TM6E7JCBYI2JV3K5IHE5ZKO52","bundle":"https://pith.science/pith/5TM6E7JCBYI2JV3K5IHE5ZKO52/bundle.json","state":"https://pith.science/pith/5TM6E7JCBYI2JV3K5IHE5ZKO52/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5TM6E7JCBYI2JV3K5IHE5ZKO52/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:5TM6E7JCBYI2JV3K5IHE5ZKO52","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":"a285d56ad0f6b878cba8bc3ae678fea5110d3bc2ae5409018b30ff4ec84a86da","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2025-06-06T07:58:37Z","title_canon_sha256":"d860fba7c5c1a1d979b6adbe2e4b2f322d7fbcc6874f0882be8ba3887be8e81d"},"schema_version":"1.0","source":{"id":"2506.05837","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.05837","created_at":"2026-07-05T11:17:10Z"},{"alias_kind":"arxiv_version","alias_value":"2506.05837v1","created_at":"2026-07-05T11:17:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.05837","created_at":"2026-07-05T11:17:10Z"},{"alias_kind":"pith_short_12","alias_value":"5TM6E7JCBYI2","created_at":"2026-07-05T11:17:10Z"},{"alias_kind":"pith_short_16","alias_value":"5TM6E7JCBYI2JV3K","created_at":"2026-07-05T11:17:10Z"},{"alias_kind":"pith_short_8","alias_value":"5TM6E7JC","created_at":"2026-07-05T11:17:10Z"}],"graph_snapshots":[{"event_id":"sha256:182e23517fe7ee415117e03e52023e534a5bd52fd28ea68c28b8c6bcc061d527","target":"graph","created_at":"2026-07-05T11:17:10Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2506.05837/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Inductive proofs can be represented as proof schemata, i.e. as parameterized sequences of proofs defined in a primitive recursive way. Applications of proof schemata can be found in the area of automated proof analysis where the schemata admit (schematic) cut-elimination and the construction of Herbrand systems. This work focuses on the expressivity of proof schemata. We show that proof schemata can simulate primitive recursive arithmetic. The translation of proofs in arithmetic to proof schemata can be considered as a crucial step in the analysis of inductive proofs.","authors_text":"Alexander Leitsch, Anela Loli\\'c, Stella Mahler","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2025-06-06T07:58:37Z","title":"Towards an Analysis of Proofs in Arithmetic"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.05837","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:daf56fb3655f84d7f110324fee03bb762f53123a4a1bae095d2fa5310a5f8463","target":"record","created_at":"2026-07-05T11:17:10Z","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":"a285d56ad0f6b878cba8bc3ae678fea5110d3bc2ae5409018b30ff4ec84a86da","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2025-06-06T07:58:37Z","title_canon_sha256":"d860fba7c5c1a1d979b6adbe2e4b2f322d7fbcc6874f0882be8ba3887be8e81d"},"schema_version":"1.0","source":{"id":"2506.05837","kind":"arxiv","version":1}},"canonical_sha256":"ecd9e27d220e11a4d76aea0e4ee54eeebb4ede72df391a9e9a723339b6c2726e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ecd9e27d220e11a4d76aea0e4ee54eeebb4ede72df391a9e9a723339b6c2726e","first_computed_at":"2026-07-05T11:17:10.995934Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:17:10.995934Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"giWbg/hSE7w2j2N/RXHQCbLZzGhc1mqAoJ4NgIqoVDeq/JaCxXD/GTuQLW4v3UxVYo9Ms32SCABl8yISAe+TAA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:17:10.996421Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.05837","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:daf56fb3655f84d7f110324fee03bb762f53123a4a1bae095d2fa5310a5f8463","sha256:182e23517fe7ee415117e03e52023e534a5bd52fd28ea68c28b8c6bcc061d527"],"state_sha256":"3634e93ea114404e75fe87986ddd77cf51d7be7f958daa2f5d93661a265b5a26"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BVG2dSNvLrxmxbI/EPnrdg//BtSz2EqhSIaR1Wd690t/zFQAizF7pFr86MV/0r8TbV0pcD2G5F+C2PjIbnQODg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T01:40:59.077419Z","bundle_sha256":"c6311570dba19ea4d2966dafb3b37f259b4fbbd1ad8dfe551e74e4866478eee6"}}