{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:EQ4SMJ6JUXCJQ6ZZU6FTDIKLHS","short_pith_number":"pith:EQ4SMJ6J","canonical_record":{"source":{"id":"2605.31485","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-29T16:08:49Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"83bb77e5219074cc50ecaff239f2b8a63447e34a1305ddae0c31906eca29c6c6","abstract_canon_sha256":"6dc8cb4720dc651aa1342e056828af5add76b32965ebbc5a48ed1b868921c720"},"schema_version":"1.0"},"canonical_sha256":"24392627c9a5c4987b39a78b31a14b3c967bf2d3aa7d8d6bde44d78a699872c5","source":{"kind":"arxiv","id":"2605.31485","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.31485","created_at":"2026-06-01T02:04:08Z"},{"alias_kind":"arxiv_version","alias_value":"2605.31485v1","created_at":"2026-06-01T02:04:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.31485","created_at":"2026-06-01T02:04:08Z"},{"alias_kind":"pith_short_12","alias_value":"EQ4SMJ6JUXCJ","created_at":"2026-06-01T02:04:08Z"},{"alias_kind":"pith_short_16","alias_value":"EQ4SMJ6JUXCJQ6ZZ","created_at":"2026-06-01T02:04:08Z"},{"alias_kind":"pith_short_8","alias_value":"EQ4SMJ6J","created_at":"2026-06-01T02:04:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:EQ4SMJ6JUXCJQ6ZZU6FTDIKLHS","target":"record","payload":{"canonical_record":{"source":{"id":"2605.31485","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-29T16:08:49Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"83bb77e5219074cc50ecaff239f2b8a63447e34a1305ddae0c31906eca29c6c6","abstract_canon_sha256":"6dc8cb4720dc651aa1342e056828af5add76b32965ebbc5a48ed1b868921c720"},"schema_version":"1.0"},"canonical_sha256":"24392627c9a5c4987b39a78b31a14b3c967bf2d3aa7d8d6bde44d78a699872c5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-01T02:04:08.559048Z","signature_b64":"SxTtjPZnXOTHp5DvQSTr2kHRBVwkjoFyojmUetfhrDlLlLm1eFKWIHy1UFRcmjjHrT+Xn7lwizg5THI9W5Y2BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"24392627c9a5c4987b39a78b31a14b3c967bf2d3aa7d8d6bde44d78a699872c5","last_reissued_at":"2026-06-01T02:04:08.558350Z","signature_status":"signed_v1","first_computed_at":"2026-06-01T02:04:08.558350Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.31485","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":"2026-06-01T02:04:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"waY+wEAUms/hwzPLBG+AGdRXoEfODmd9a07gd9PJD6nYCUs/NglwTgbxPfFpC9cU8Ay0WA5BjtVlwv/+nQFHCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T04:35:41.936560Z"},"content_sha256":"d0eddc6a7b12981b1a0dec78f01025f90dbda2ee5b0ecf53b51ee96c8bdaecbf","schema_version":"1.0","event_id":"sha256:d0eddc6a7b12981b1a0dec78f01025f90dbda2ee5b0ecf53b51ee96c8bdaecbf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:EQ4SMJ6JUXCJQ6ZZU6FTDIKLHS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Graphical einops: bridging tensor networks and computation graphs","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"cs.LG","authors_text":"Nikhil Khatri, Vincent Wang-Ma\\'scianica","submitted_at":"2026-05-29T16:08:49Z","abstract_excerpt":"Architecture diagrams are ubiquitous in deep learning, but they are usually only representational: the tensor-program identities they suggest are still proved by prose and tensor-axis manipulation. We introduce a formal graphical calculus for the structural fragment of tensor programming underlying einops, making such diagrams proof-enabling. Our calculus represents tensor axes as nested graded tubes around a base type. The tube boundary recovers the undirected tensor-network view of axes, while the directed interior retains the operational reading of computation graphs. The key rewrite is gra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.31485","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/2605.31485/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":"2026-06-01T02:04:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rQefQOEzju+cLX1Ae+A9BSiOc1kGdGlRnhGaVCOaZFgW93O9MZclOsMJmLuBWJPNH/U/RWlusKKudFaicKmoDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T04:35:41.937010Z"},"content_sha256":"d99e1422f4698391cb78f1a1d07444743d4f510d112de31a0ea95d2ffefd77c9","schema_version":"1.0","event_id":"sha256:d99e1422f4698391cb78f1a1d07444743d4f510d112de31a0ea95d2ffefd77c9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EQ4SMJ6JUXCJQ6ZZU6FTDIKLHS/bundle.json","state_url":"https://pith.science/pith/EQ4SMJ6JUXCJQ6ZZU6FTDIKLHS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EQ4SMJ6JUXCJQ6ZZU6FTDIKLHS/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":"2026-06-30T04:35:41Z","links":{"resolver":"https://pith.science/pith/EQ4SMJ6JUXCJQ6ZZU6FTDIKLHS","bundle":"https://pith.science/pith/EQ4SMJ6JUXCJQ6ZZU6FTDIKLHS/bundle.json","state":"https://pith.science/pith/EQ4SMJ6JUXCJQ6ZZU6FTDIKLHS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EQ4SMJ6JUXCJQ6ZZU6FTDIKLHS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:EQ4SMJ6JUXCJQ6ZZU6FTDIKLHS","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":"6dc8cb4720dc651aa1342e056828af5add76b32965ebbc5a48ed1b868921c720","cross_cats_sorted":["math.CT"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-29T16:08:49Z","title_canon_sha256":"83bb77e5219074cc50ecaff239f2b8a63447e34a1305ddae0c31906eca29c6c6"},"schema_version":"1.0","source":{"id":"2605.31485","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.31485","created_at":"2026-06-01T02:04:08Z"},{"alias_kind":"arxiv_version","alias_value":"2605.31485v1","created_at":"2026-06-01T02:04:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.31485","created_at":"2026-06-01T02:04:08Z"},{"alias_kind":"pith_short_12","alias_value":"EQ4SMJ6JUXCJ","created_at":"2026-06-01T02:04:08Z"},{"alias_kind":"pith_short_16","alias_value":"EQ4SMJ6JUXCJQ6ZZ","created_at":"2026-06-01T02:04:08Z"},{"alias_kind":"pith_short_8","alias_value":"EQ4SMJ6J","created_at":"2026-06-01T02:04:08Z"}],"graph_snapshots":[{"event_id":"sha256:d99e1422f4698391cb78f1a1d07444743d4f510d112de31a0ea95d2ffefd77c9","target":"graph","created_at":"2026-06-01T02:04:08Z","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/2605.31485/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Architecture diagrams are ubiquitous in deep learning, but they are usually only representational: the tensor-program identities they suggest are still proved by prose and tensor-axis manipulation. We introduce a formal graphical calculus for the structural fragment of tensor programming underlying einops, making such diagrams proof-enabling. Our calculus represents tensor axes as nested graded tubes around a base type. The tube boundary recovers the undirected tensor-network view of axes, while the directed interior retains the operational reading of computation graphs. The key rewrite is gra","authors_text":"Nikhil Khatri, Vincent Wang-Ma\\'scianica","cross_cats":["math.CT"],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-29T16:08:49Z","title":"Graphical einops: bridging tensor networks and computation graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.31485","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:d0eddc6a7b12981b1a0dec78f01025f90dbda2ee5b0ecf53b51ee96c8bdaecbf","target":"record","created_at":"2026-06-01T02:04:08Z","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":"6dc8cb4720dc651aa1342e056828af5add76b32965ebbc5a48ed1b868921c720","cross_cats_sorted":["math.CT"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-29T16:08:49Z","title_canon_sha256":"83bb77e5219074cc50ecaff239f2b8a63447e34a1305ddae0c31906eca29c6c6"},"schema_version":"1.0","source":{"id":"2605.31485","kind":"arxiv","version":1}},"canonical_sha256":"24392627c9a5c4987b39a78b31a14b3c967bf2d3aa7d8d6bde44d78a699872c5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"24392627c9a5c4987b39a78b31a14b3c967bf2d3aa7d8d6bde44d78a699872c5","first_computed_at":"2026-06-01T02:04:08.558350Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-01T02:04:08.558350Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SxTtjPZnXOTHp5DvQSTr2kHRBVwkjoFyojmUetfhrDlLlLm1eFKWIHy1UFRcmjjHrT+Xn7lwizg5THI9W5Y2BQ==","signature_status":"signed_v1","signed_at":"2026-06-01T02:04:08.559048Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.31485","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d0eddc6a7b12981b1a0dec78f01025f90dbda2ee5b0ecf53b51ee96c8bdaecbf","sha256:d99e1422f4698391cb78f1a1d07444743d4f510d112de31a0ea95d2ffefd77c9"],"state_sha256":"870650cb596371126352b9ffb3d32a042ac83aa3676ed5e0951371da531caacc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SrOBED4yDK4LexNRnUTK102Act6K2XxmCP0HbzzPmCUvlyOVEdiEMasV/nyjBG9zmlIEONEIRZdPBexQ50SaDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T04:35:41.939174Z","bundle_sha256":"ca09bc3ea76c8f62111dd0895a42c0f61a028a86a55402e5b63f386fad445e51"}}