{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:EGZEZEKN2TEI774NNOFPGUPMAB","short_pith_number":"pith:EGZEZEKN","canonical_record":{"source":{"id":"2504.14340","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.PL","submitted_at":"2025-04-19T16:15:11Z","cross_cats_sorted":[],"title_canon_sha256":"db92b330ec96a0194a37007ce4ef6782b3c5d8dda7ba4e9f6d75b183c3fdee3f","abstract_canon_sha256":"e254a4d6ab60c165e279aafdeab0a6850021b813c503e35f84e988eb4c0553a1"},"schema_version":"1.0"},"canonical_sha256":"21b24c914dd4c88fff8d6b8af351ec007824b00bc5b6746d5853118d1de563ed","source":{"kind":"arxiv","id":"2504.14340","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.14340","created_at":"2026-07-05T10:51:42Z"},{"alias_kind":"arxiv_version","alias_value":"2504.14340v1","created_at":"2026-07-05T10:51:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.14340","created_at":"2026-07-05T10:51:42Z"},{"alias_kind":"pith_short_12","alias_value":"EGZEZEKN2TEI","created_at":"2026-07-05T10:51:42Z"},{"alias_kind":"pith_short_16","alias_value":"EGZEZEKN2TEI774N","created_at":"2026-07-05T10:51:42Z"},{"alias_kind":"pith_short_8","alias_value":"EGZEZEKN","created_at":"2026-07-05T10:51:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:EGZEZEKN2TEI774NNOFPGUPMAB","target":"record","payload":{"canonical_record":{"source":{"id":"2504.14340","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.PL","submitted_at":"2025-04-19T16:15:11Z","cross_cats_sorted":[],"title_canon_sha256":"db92b330ec96a0194a37007ce4ef6782b3c5d8dda7ba4e9f6d75b183c3fdee3f","abstract_canon_sha256":"e254a4d6ab60c165e279aafdeab0a6850021b813c503e35f84e988eb4c0553a1"},"schema_version":"1.0"},"canonical_sha256":"21b24c914dd4c88fff8d6b8af351ec007824b00bc5b6746d5853118d1de563ed","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:51:42.064209Z","signature_b64":"a0cmaUgNE8fyOLEBcg9dn2TEbfZX9dFcB2o3BycATQ21n0sMTOyixfCWPt4RmnKvW+kd+GSzSOxQcZat02aVAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"21b24c914dd4c88fff8d6b8af351ec007824b00bc5b6746d5853118d1de563ed","last_reissued_at":"2026-07-05T10:51:42.063688Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:51:42.063688Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2504.14340","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":"2026-07-05T10:51:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L3RqIPfV9arb48eTK02vojRWYB/u5C7kKm1M+ih2/cxJmrJgPzdBPhLAqiZSMDs8VSV/Vrd2RTh6U4IyqaucAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T06:18:16.495136Z"},"content_sha256":"70e553c69701a1ab97d3f12d9dc0092e0f33c27479d7fa30b7446c8320a97b01","schema_version":"1.0","event_id":"sha256:70e553c69701a1ab97d3f12d9dc0092e0f33c27479d7fa30b7446c8320a97b01"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:EGZEZEKN2TEI774NNOFPGUPMAB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Omelets Need Onions: E-graphs Modulo Theories via Bottom-up E-matching","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.PL","authors_text":"Philip Zucker","submitted_at":"2025-04-19T16:15:11Z","abstract_excerpt":"E-graphs are a data structure for equational reasoning and optimization over ground terms. One of the benefits of e-graph rewriting is that it can declaratively handle useful but difficult to orient identities like associativity and commutativity (AC) in a generic way. However, using these generic mechanisms is more computationally expensive than using bespoke routines on terms containing sets, multi-sets, linear expressions, polynomials, and binders. A natural question arises: How can one combine the generic capabilities of e-graph rewriting with these specialized theories. This paper discuss"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.14340","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/2504.14340/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":"2026-07-05T10:51:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"91I+4xPb8ILSO6uBUDKK0yxnK9I9DM+npzdKgXQ0bbXBxV8VefuV3YCcacZBLBwOGxRGMWmg6NZ/o9srKapECw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T06:18:16.495630Z"},"content_sha256":"5d5c692db874c70b150f4fe198384396f227cfcf9594c3aee81a03a89602ab3e","schema_version":"1.0","event_id":"sha256:5d5c692db874c70b150f4fe198384396f227cfcf9594c3aee81a03a89602ab3e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EGZEZEKN2TEI774NNOFPGUPMAB/bundle.json","state_url":"https://pith.science/pith/EGZEZEKN2TEI774NNOFPGUPMAB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EGZEZEKN2TEI774NNOFPGUPMAB/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":"2026-08-05T06:18:16Z","links":{"resolver":"https://pith.science/pith/EGZEZEKN2TEI774NNOFPGUPMAB","bundle":"https://pith.science/pith/EGZEZEKN2TEI774NNOFPGUPMAB/bundle.json","state":"https://pith.science/pith/EGZEZEKN2TEI774NNOFPGUPMAB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EGZEZEKN2TEI774NNOFPGUPMAB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:EGZEZEKN2TEI774NNOFPGUPMAB","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":"e254a4d6ab60c165e279aafdeab0a6850021b813c503e35f84e988eb4c0553a1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.PL","submitted_at":"2025-04-19T16:15:11Z","title_canon_sha256":"db92b330ec96a0194a37007ce4ef6782b3c5d8dda7ba4e9f6d75b183c3fdee3f"},"schema_version":"1.0","source":{"id":"2504.14340","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.14340","created_at":"2026-07-05T10:51:42Z"},{"alias_kind":"arxiv_version","alias_value":"2504.14340v1","created_at":"2026-07-05T10:51:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.14340","created_at":"2026-07-05T10:51:42Z"},{"alias_kind":"pith_short_12","alias_value":"EGZEZEKN2TEI","created_at":"2026-07-05T10:51:42Z"},{"alias_kind":"pith_short_16","alias_value":"EGZEZEKN2TEI774N","created_at":"2026-07-05T10:51:42Z"},{"alias_kind":"pith_short_8","alias_value":"EGZEZEKN","created_at":"2026-07-05T10:51:42Z"}],"graph_snapshots":[{"event_id":"sha256:5d5c692db874c70b150f4fe198384396f227cfcf9594c3aee81a03a89602ab3e","target":"graph","created_at":"2026-07-05T10:51:42Z","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/2504.14340/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"E-graphs are a data structure for equational reasoning and optimization over ground terms. One of the benefits of e-graph rewriting is that it can declaratively handle useful but difficult to orient identities like associativity and commutativity (AC) in a generic way. However, using these generic mechanisms is more computationally expensive than using bespoke routines on terms containing sets, multi-sets, linear expressions, polynomials, and binders. A natural question arises: How can one combine the generic capabilities of e-graph rewriting with these specialized theories. This paper discuss","authors_text":"Philip Zucker","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.PL","submitted_at":"2025-04-19T16:15:11Z","title":"Omelets Need Onions: E-graphs Modulo Theories via Bottom-up E-matching"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.14340","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":"sha256:70e553c69701a1ab97d3f12d9dc0092e0f33c27479d7fa30b7446c8320a97b01","target":"record","created_at":"2026-07-05T10:51:42Z","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":"e254a4d6ab60c165e279aafdeab0a6850021b813c503e35f84e988eb4c0553a1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.PL","submitted_at":"2025-04-19T16:15:11Z","title_canon_sha256":"db92b330ec96a0194a37007ce4ef6782b3c5d8dda7ba4e9f6d75b183c3fdee3f"},"schema_version":"1.0","source":{"id":"2504.14340","kind":"arxiv","version":1}},"canonical_sha256":"21b24c914dd4c88fff8d6b8af351ec007824b00bc5b6746d5853118d1de563ed","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"21b24c914dd4c88fff8d6b8af351ec007824b00bc5b6746d5853118d1de563ed","first_computed_at":"2026-07-05T10:51:42.063688Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:51:42.063688Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"a0cmaUgNE8fyOLEBcg9dn2TEbfZX9dFcB2o3BycATQ21n0sMTOyixfCWPt4RmnKvW+kd+GSzSOxQcZat02aVAA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:51:42.064209Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.14340","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:70e553c69701a1ab97d3f12d9dc0092e0f33c27479d7fa30b7446c8320a97b01","sha256:5d5c692db874c70b150f4fe198384396f227cfcf9594c3aee81a03a89602ab3e"],"state_sha256":"f859b56e31417378a7b6cf8ddd73b7b64f18aad3489bf57627e2566a12fffa85"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"25/WAJrn8qqQNoofEfiI/aV4CLGunOLfC/hPnEzo6QkWcqMCWgzclKNINMgx4gqD6vZpMGK69jEtZqVAvl++Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T06:18:16.500557Z","bundle_sha256":"87a250ab0cb476dddfd94da1d714fc9dec3111dd5982ef95cc8c3624cd014c27"}}