{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:W7UWNYMS44KCD4KWBDOBGTKVJN","short_pith_number":"pith:W7UWNYMS","canonical_record":{"source":{"id":"1502.05860","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2015-02-20T12:53:38Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"095aa2174ad0d3ed9ab005f54f3c0126de731f3e6563b0144c9f9d0b15be544c","abstract_canon_sha256":"f6896a67eca10024ba36d56adc0d902bd9eb4e41ead9717375088ef29b680f1b"},"schema_version":"1.0"},"canonical_sha256":"b7e966e192e71421f15608dc134d554b40d0d4c5de3f9785756ce7fe09767a45","source":{"kind":"arxiv","id":"1502.05860","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.05860","created_at":"2026-05-17T23:51:23Z"},{"alias_kind":"arxiv_version","alias_value":"1502.05860v2","created_at":"2026-05-17T23:51:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.05860","created_at":"2026-05-17T23:51:23Z"},{"alias_kind":"pith_short_12","alias_value":"W7UWNYMS44KC","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"W7UWNYMS44KCD4KW","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"W7UWNYMS","created_at":"2026-05-18T12:29:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:W7UWNYMS44KCD4KWBDOBGTKVJN","target":"record","payload":{"canonical_record":{"source":{"id":"1502.05860","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2015-02-20T12:53:38Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"095aa2174ad0d3ed9ab005f54f3c0126de731f3e6563b0144c9f9d0b15be544c","abstract_canon_sha256":"f6896a67eca10024ba36d56adc0d902bd9eb4e41ead9717375088ef29b680f1b"},"schema_version":"1.0"},"canonical_sha256":"b7e966e192e71421f15608dc134d554b40d0d4c5de3f9785756ce7fe09767a45","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:23.949501Z","signature_b64":"vZGRfGz1nHnPmUsRnEfg+7CD4adCMENPnLjwGaesvjpgMKaVzpK3wosy/vTYBQCpFdqcg7SpAGPpxCrYooFkBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b7e966e192e71421f15608dc134d554b40d0d4c5de3f9785756ce7fe09767a45","last_reissued_at":"2026-05-17T23:51:23.948894Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:23.948894Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.05860","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":"2026-05-17T23:51:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SrtfaBUvB609LrNHftcqB4rwiK6XgfHNAdroxuwFaatib/tjG3hLCNUcYPQq19V9ur1HgIQoxwsc9afjVK9lDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T13:56:03.520930Z"},"content_sha256":"9f19ffbd9a258f9e92e6c4258142a429fabb2270d5429a06969b5d3820386d30","schema_version":"1.0","event_id":"sha256:9f19ffbd9a258f9e92e6c4258142a429fabb2270d5429a06969b5d3820386d30"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:W7UWNYMS44KCD4KWBDOBGTKVJN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the relative proof complexity of deep inference via atomic flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"cs.LO","authors_text":"Anupam Das (\\'Ecole Normale Sup\\'erieure de Lyon (ENS Lyon), France)","submitted_at":"2015-02-20T12:53:38Z","abstract_excerpt":"We consider the proof complexity of the minimal complete fragment, KS, of standard deep inference systems for propositional logic. To examine the size of proofs we employ atomic flows, diagrams that trace structural changes through a proof but ignore logical information. As results we obtain a polynomial simulation of versions of Resolution, along with some extensions. We also show that these systems, as well as bounded-depth Frege systems, cannot polynomially simulate KS, by giving polynomial-size proofs of certain variants of the propositional pigeonhole principle in KS."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.05860","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":"2026-05-17T23:51:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mUuKbwQ8fmtt6wYFn7dWwnE7/zwJt2ciL22nO7flTih2dOqertisws1aXV3cUavahgGYaK6yQZNkcNtgrc+WBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T13:56:03.521271Z"},"content_sha256":"e5787dc85ffcf0d5962bca4953824712082ca12a0ea85129e88de93e839b83f1","schema_version":"1.0","event_id":"sha256:e5787dc85ffcf0d5962bca4953824712082ca12a0ea85129e88de93e839b83f1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W7UWNYMS44KCD4KWBDOBGTKVJN/bundle.json","state_url":"https://pith.science/pith/W7UWNYMS44KCD4KWBDOBGTKVJN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W7UWNYMS44KCD4KWBDOBGTKVJN/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":"2026-06-09T13:56:03Z","links":{"resolver":"https://pith.science/pith/W7UWNYMS44KCD4KWBDOBGTKVJN","bundle":"https://pith.science/pith/W7UWNYMS44KCD4KWBDOBGTKVJN/bundle.json","state":"https://pith.science/pith/W7UWNYMS44KCD4KWBDOBGTKVJN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W7UWNYMS44KCD4KWBDOBGTKVJN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:W7UWNYMS44KCD4KWBDOBGTKVJN","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":"f6896a67eca10024ba36d56adc0d902bd9eb4e41ead9717375088ef29b680f1b","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2015-02-20T12:53:38Z","title_canon_sha256":"095aa2174ad0d3ed9ab005f54f3c0126de731f3e6563b0144c9f9d0b15be544c"},"schema_version":"1.0","source":{"id":"1502.05860","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.05860","created_at":"2026-05-17T23:51:23Z"},{"alias_kind":"arxiv_version","alias_value":"1502.05860v2","created_at":"2026-05-17T23:51:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.05860","created_at":"2026-05-17T23:51:23Z"},{"alias_kind":"pith_short_12","alias_value":"W7UWNYMS44KC","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"W7UWNYMS44KCD4KW","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"W7UWNYMS","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:e5787dc85ffcf0d5962bca4953824712082ca12a0ea85129e88de93e839b83f1","target":"graph","created_at":"2026-05-17T23:51:23Z","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 consider the proof complexity of the minimal complete fragment, KS, of standard deep inference systems for propositional logic. To examine the size of proofs we employ atomic flows, diagrams that trace structural changes through a proof but ignore logical information. As results we obtain a polynomial simulation of versions of Resolution, along with some extensions. We also show that these systems, as well as bounded-depth Frege systems, cannot polynomially simulate KS, by giving polynomial-size proofs of certain variants of the propositional pigeonhole principle in KS.","authors_text":"Anupam Das (\\'Ecole Normale Sup\\'erieure de Lyon (ENS Lyon), France)","cross_cats":["math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2015-02-20T12:53:38Z","title":"On the relative proof complexity of deep inference via atomic flows"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.05860","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":"sha256:9f19ffbd9a258f9e92e6c4258142a429fabb2270d5429a06969b5d3820386d30","target":"record","created_at":"2026-05-17T23:51:23Z","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":"f6896a67eca10024ba36d56adc0d902bd9eb4e41ead9717375088ef29b680f1b","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2015-02-20T12:53:38Z","title_canon_sha256":"095aa2174ad0d3ed9ab005f54f3c0126de731f3e6563b0144c9f9d0b15be544c"},"schema_version":"1.0","source":{"id":"1502.05860","kind":"arxiv","version":2}},"canonical_sha256":"b7e966e192e71421f15608dc134d554b40d0d4c5de3f9785756ce7fe09767a45","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b7e966e192e71421f15608dc134d554b40d0d4c5de3f9785756ce7fe09767a45","first_computed_at":"2026-05-17T23:51:23.948894Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:23.948894Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vZGRfGz1nHnPmUsRnEfg+7CD4adCMENPnLjwGaesvjpgMKaVzpK3wosy/vTYBQCpFdqcg7SpAGPpxCrYooFkBA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:23.949501Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.05860","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9f19ffbd9a258f9e92e6c4258142a429fabb2270d5429a06969b5d3820386d30","sha256:e5787dc85ffcf0d5962bca4953824712082ca12a0ea85129e88de93e839b83f1"],"state_sha256":"0304043d89ba8e85ea410eafb67fdd9df348e58ddd1afdf736ecf52ee9d06652"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YLQlzrYdQ0afVs/d+2abWejFHrZSUaR0/F1X/Z2DdZfMBc251sctlLPeohpD/5F3Z6KF/g8Ioto2ei6EjS7LBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T13:56:03.523637Z","bundle_sha256":"275579775172612fa53428d5ef667bf0aa34b0dfaf861ed2864b78db4d555df8"}}