{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:AIK7MBYVE2IDH4DNFISFIJQVYW","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":"7c419e6df0cc090712c7bb2d0d25191966f4f8a331b31b75049d5b837a2a89f5","cross_cats_sorted":["math-ph","math.MP","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-12-11T10:36:44Z","title_canon_sha256":"db73d266f3fb8fbacf7c336db74c8c841e287cb6e27e11f33a7e42c214b0e1a0"},"schema_version":"1.0","source":{"id":"1212.2376","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.2376","created_at":"2026-05-18T03:38:45Z"},{"alias_kind":"arxiv_version","alias_value":"1212.2376v1","created_at":"2026-05-18T03:38:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.2376","created_at":"2026-05-18T03:38:45Z"},{"alias_kind":"pith_short_12","alias_value":"AIK7MBYVE2ID","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"AIK7MBYVE2IDH4DN","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"AIK7MBYV","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:f8421767d7725421e91dfc15c325296b59f8204bb0f95ee2be44d8fcf070aae3","target":"graph","created_at":"2026-05-18T03:38:45Z","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":"In this paper, the notion of strongly typed language will be borrowed from the field of computer programming to introduce a calculational framework for linear algebra and tensor calculus for the purpose of detecting errors resulting from inherent misuse of objects and for finding natural formulations of various objects. A tensor bundle formalism, crucially relying on the notion of pullback bundle, will be used to create a rich type system with which to distinguish objects. The type system and relevant notation is designed to \"telescope\" to accomodate a level of detail appropriate to a set of c","authors_text":"Victor Dods","cross_cats":["math-ph","math.MP","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-12-11T10:36:44Z","title":"Riemannian Calculus of Variations using Strongly Typed Tensor Calculus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.2376","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:cada54616128e500d8530d175598355f9b7188c61a9ad0b3191f148b4a79c9c8","target":"record","created_at":"2026-05-18T03:38:45Z","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":"7c419e6df0cc090712c7bb2d0d25191966f4f8a331b31b75049d5b837a2a89f5","cross_cats_sorted":["math-ph","math.MP","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-12-11T10:36:44Z","title_canon_sha256":"db73d266f3fb8fbacf7c336db74c8c841e287cb6e27e11f33a7e42c214b0e1a0"},"schema_version":"1.0","source":{"id":"1212.2376","kind":"arxiv","version":1}},"canonical_sha256":"0215f60715269033f06d2a24542615c5be9d39124c16f900afd93aa8c7d944a4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0215f60715269033f06d2a24542615c5be9d39124c16f900afd93aa8c7d944a4","first_computed_at":"2026-05-18T03:38:45.091531Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:45.091531Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9c36uc8RqydDX4QdmP89nu/fXNelArPqc8J/YSZ/WIYwM+gX7/Z35pAnDTgmxJn7V2x8yNehSs5eQuEVeVCDAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:45.092215Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.2376","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cada54616128e500d8530d175598355f9b7188c61a9ad0b3191f148b4a79c9c8","sha256:f8421767d7725421e91dfc15c325296b59f8204bb0f95ee2be44d8fcf070aae3"],"state_sha256":"61274b44d1c01a0d18a24475d5a66157b22da6cf771287c79e1b55701db7dc90"}