{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:P7TOEY4FUFEX5TVQV2LMBDGCTB","short_pith_number":"pith:P7TOEY4F","canonical_record":{"source":{"id":"2404.11591","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2024-04-17T17:42:48Z","cross_cats_sorted":[],"title_canon_sha256":"c9eec3f6c868d89624caeaa006e04c2a86e6311054098952b2d4177f1af78345","abstract_canon_sha256":"81922fc0f85b2a1a040995d09616706e81f8ccb8a2e501110806d344ec8b46b2"},"schema_version":"1.0"},"canonical_sha256":"7fe6e26385a1497eceb0ae96c08cc2985081775c3c47b1901fbe6134701b8697","source":{"kind":"arxiv","id":"2404.11591","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.11591","created_at":"2026-05-28T01:04:24Z"},{"alias_kind":"arxiv_version","alias_value":"2404.11591v3","created_at":"2026-05-28T01:04:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.11591","created_at":"2026-05-28T01:04:24Z"},{"alias_kind":"pith_short_12","alias_value":"P7TOEY4FUFEX","created_at":"2026-05-28T01:04:24Z"},{"alias_kind":"pith_short_16","alias_value":"P7TOEY4FUFEX5TVQ","created_at":"2026-05-28T01:04:24Z"},{"alias_kind":"pith_short_8","alias_value":"P7TOEY4F","created_at":"2026-05-28T01:04:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:P7TOEY4FUFEX5TVQV2LMBDGCTB","target":"record","payload":{"canonical_record":{"source":{"id":"2404.11591","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2024-04-17T17:42:48Z","cross_cats_sorted":[],"title_canon_sha256":"c9eec3f6c868d89624caeaa006e04c2a86e6311054098952b2d4177f1af78345","abstract_canon_sha256":"81922fc0f85b2a1a040995d09616706e81f8ccb8a2e501110806d344ec8b46b2"},"schema_version":"1.0"},"canonical_sha256":"7fe6e26385a1497eceb0ae96c08cc2985081775c3c47b1901fbe6134701b8697","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-28T01:04:24.144776Z","signature_b64":"62IbbCxr0nl7PIz6GsOJWpXKgILqqHnU1eZoC/Z/K3oWlaT5GPtCsk35u7rsJTsGfzDnhH5BiIzwcdv5952rCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7fe6e26385a1497eceb0ae96c08cc2985081775c3c47b1901fbe6134701b8697","last_reissued_at":"2026-05-28T01:04:24.144189Z","signature_status":"signed_v1","first_computed_at":"2026-05-28T01:04:24.144189Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2404.11591","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":"2026-05-28T01:04:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MLuR4uajSQGL8SDXTiYOH/UIY/984P7Vw3eOfkMoI2xWTL+dERctVfhje4J6TvlqVuqYdC1wGanb2LiMkRzBDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T09:00:32.475255Z"},"content_sha256":"fc5136e99afe870e7a273715f7cda08a06321d72b38a6673d0621d5dee9cdb59","schema_version":"1.0","event_id":"sha256:fc5136e99afe870e7a273715f7cda08a06321d72b38a6673d0621d5dee9cdb59"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:P7TOEY4FUFEX5TVQV2LMBDGCTB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The EDGE Language: Extended General Einsums for Graph Algorithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The EDGE language expresses graph algorithms as extended Einsum tensor expressions.","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Joel S. Emer, John D. Owens, Michael Pellauer, Nandeeka Nayak, Serban D. Porumbescu, Toluwanimi O. Odemuyiwa","submitted_at":"2024-04-17T17:42:48Z","abstract_excerpt":"In this work, we propose a unified abstraction for graph algorithms: the Extended General Einsums language, or EDGE. The EDGE language expresses graph algorithms in the language of tensor algebra, providing a rigorous, succinct, and expressive mathematical framework. EDGE leverages two ideas: (1) the well-known foundations provided by the graph-matrix duality, where a graph is simply a 2D tensor, and (2) the power and expressivity of Einsum notation in the tensor algebra world. In this work, we describe our design goals for EDGE and walk through the extensions we add to Einsums to support more"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The EDGE language expresses graph algorithms in the language of tensor algebra, providing a rigorous, succinct, and expressive mathematical framework that allows researchers to more easily compare algorithms, factor complexity, and discover variants through algebraic manipulations.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the proposed extensions to Einsum notation are sufficient to capture the complex operations common in graph algorithms without losing expressivity or requiring ad-hoc additions beyond those described.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"EDGE extends Einsum notation with graph-specific operations to create a unified tensor-algebra framework for expressing and manipulating graph algorithms.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The EDGE language expresses graph algorithms as extended Einsum tensor expressions.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"24fd4fffa0661d9a839542f8c76933d9ba6d4204aa3a356c608eb806f52ea048"},"source":{"id":"2404.11591","kind":"arxiv","version":3},"verdict":{"id":"16f831e5-0679-477a-a61f-f4416e2f6b02","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-24T01:34:56.045373Z","strongest_claim":"The EDGE language expresses graph algorithms in the language of tensor algebra, providing a rigorous, succinct, and expressive mathematical framework that allows researchers to more easily compare algorithms, factor complexity, and discover variants through algebraic manipulations.","one_line_summary":"EDGE extends Einsum notation with graph-specific operations to create a unified tensor-algebra framework for expressing and manipulating graph algorithms.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the proposed extensions to Einsum notation are sufficient to capture the complex operations common in graph algorithms without losing expressivity or requiring ad-hoc additions beyond those described.","pith_extraction_headline":"The EDGE language expresses graph algorithms as extended Einsum tensor expressions."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2404.11591/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":"16f831e5-0679-477a-a61f-f4416e2f6b02"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-28T01:04:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Tuwihj7rdeSVXoyWQAij2tfa72HueTY3TvqL1+b+MhtoF301QP/GinAMYoOANKE7VwmZGAx1sGh2/nooj0zKBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T09:00:32.476162Z"},"content_sha256":"5e7ef3cf3617decae2d0e4c3931a4a910a5d1e8f68568944e50c67c7ff0f98ea","schema_version":"1.0","event_id":"sha256:5e7ef3cf3617decae2d0e4c3931a4a910a5d1e8f68568944e50c67c7ff0f98ea"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P7TOEY4FUFEX5TVQV2LMBDGCTB/bundle.json","state_url":"https://pith.science/pith/P7TOEY4FUFEX5TVQV2LMBDGCTB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P7TOEY4FUFEX5TVQV2LMBDGCTB/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":"2026-06-10T09:00:32Z","links":{"resolver":"https://pith.science/pith/P7TOEY4FUFEX5TVQV2LMBDGCTB","bundle":"https://pith.science/pith/P7TOEY4FUFEX5TVQV2LMBDGCTB/bundle.json","state":"https://pith.science/pith/P7TOEY4FUFEX5TVQV2LMBDGCTB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P7TOEY4FUFEX5TVQV2LMBDGCTB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:P7TOEY4FUFEX5TVQV2LMBDGCTB","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":"81922fc0f85b2a1a040995d09616706e81f8ccb8a2e501110806d344ec8b46b2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2024-04-17T17:42:48Z","title_canon_sha256":"c9eec3f6c868d89624caeaa006e04c2a86e6311054098952b2d4177f1af78345"},"schema_version":"1.0","source":{"id":"2404.11591","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.11591","created_at":"2026-05-28T01:04:24Z"},{"alias_kind":"arxiv_version","alias_value":"2404.11591v3","created_at":"2026-05-28T01:04:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.11591","created_at":"2026-05-28T01:04:24Z"},{"alias_kind":"pith_short_12","alias_value":"P7TOEY4FUFEX","created_at":"2026-05-28T01:04:24Z"},{"alias_kind":"pith_short_16","alias_value":"P7TOEY4FUFEX5TVQ","created_at":"2026-05-28T01:04:24Z"},{"alias_kind":"pith_short_8","alias_value":"P7TOEY4F","created_at":"2026-05-28T01:04:24Z"}],"graph_snapshots":[{"event_id":"sha256:5e7ef3cf3617decae2d0e4c3931a4a910a5d1e8f68568944e50c67c7ff0f98ea","target":"graph","created_at":"2026-05-28T01:04:24Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"The EDGE language expresses graph algorithms in the language of tensor algebra, providing a rigorous, succinct, and expressive mathematical framework that allows researchers to more easily compare algorithms, factor complexity, and discover variants through algebraic manipulations."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"That the proposed extensions to Einsum notation are sufficient to capture the complex operations common in graph algorithms without losing expressivity or requiring ad-hoc additions beyond those described."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"EDGE extends Einsum notation with graph-specific operations to create a unified tensor-algebra framework for expressing and manipulating graph algorithms."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"The EDGE language expresses graph algorithms as extended Einsum tensor expressions."}],"snapshot_sha256":"24fd4fffa0661d9a839542f8c76933d9ba6d4204aa3a356c608eb806f52ea048"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2404.11591/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this work, we propose a unified abstraction for graph algorithms: the Extended General Einsums language, or EDGE. The EDGE language expresses graph algorithms in the language of tensor algebra, providing a rigorous, succinct, and expressive mathematical framework. EDGE leverages two ideas: (1) the well-known foundations provided by the graph-matrix duality, where a graph is simply a 2D tensor, and (2) the power and expressivity of Einsum notation in the tensor algebra world. In this work, we describe our design goals for EDGE and walk through the extensions we add to Einsums to support more","authors_text":"Joel S. Emer, John D. Owens, Michael Pellauer, Nandeeka Nayak, Serban D. Porumbescu, Toluwanimi O. Odemuyiwa","cross_cats":[],"headline":"The EDGE language expresses graph algorithms as extended Einsum tensor expressions.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2024-04-17T17:42:48Z","title":"The EDGE Language: Extended General Einsums for Graph Algorithms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.11591","kind":"arxiv","version":3},"verdict":{"created_at":"2026-05-24T01:34:56.045373Z","id":"16f831e5-0679-477a-a61f-f4416e2f6b02","model_set":{"reader":"grok-4.3"},"one_line_summary":"EDGE extends Einsum notation with graph-specific operations to create a unified tensor-algebra framework for expressing and manipulating graph algorithms.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"The EDGE language expresses graph algorithms as extended Einsum tensor expressions.","strongest_claim":"The EDGE language expresses graph algorithms in the language of tensor algebra, providing a rigorous, succinct, and expressive mathematical framework that allows researchers to more easily compare algorithms, factor complexity, and discover variants through algebraic manipulations.","weakest_assumption":"That the proposed extensions to Einsum notation are sufficient to capture the complex operations common in graph algorithms without losing expressivity or requiring ad-hoc additions beyond those described."}},"verdict_id":"16f831e5-0679-477a-a61f-f4416e2f6b02"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:fc5136e99afe870e7a273715f7cda08a06321d72b38a6673d0621d5dee9cdb59","target":"record","created_at":"2026-05-28T01:04:24Z","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":"81922fc0f85b2a1a040995d09616706e81f8ccb8a2e501110806d344ec8b46b2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2024-04-17T17:42:48Z","title_canon_sha256":"c9eec3f6c868d89624caeaa006e04c2a86e6311054098952b2d4177f1af78345"},"schema_version":"1.0","source":{"id":"2404.11591","kind":"arxiv","version":3}},"canonical_sha256":"7fe6e26385a1497eceb0ae96c08cc2985081775c3c47b1901fbe6134701b8697","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7fe6e26385a1497eceb0ae96c08cc2985081775c3c47b1901fbe6134701b8697","first_computed_at":"2026-05-28T01:04:24.144189Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-28T01:04:24.144189Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"62IbbCxr0nl7PIz6GsOJWpXKgILqqHnU1eZoC/Z/K3oWlaT5GPtCsk35u7rsJTsGfzDnhH5BiIzwcdv5952rCQ==","signature_status":"signed_v1","signed_at":"2026-05-28T01:04:24.144776Z","signed_message":"canonical_sha256_bytes"},"source_id":"2404.11591","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fc5136e99afe870e7a273715f7cda08a06321d72b38a6673d0621d5dee9cdb59","sha256:5e7ef3cf3617decae2d0e4c3931a4a910a5d1e8f68568944e50c67c7ff0f98ea"],"state_sha256":"33f196dcb9ddac29b0083c528da1c60d26da0de63f580f5208ec0bbf5123a842"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FcSL3tIP7xSj4wiFcFP9QxeOFGswSBzD5/+Z0cm36GDS+DzmwSw6jbGjPy8CxDmm0cG6eMwLte/3BjkoujWhCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T09:00:32.480365Z","bundle_sha256":"874dae2a1bd5c0cdbb1862ab10b4d6aa1b3426f2aa38853bc81791ec74659bc0"}}