{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:M2A5OJJSSPTN2TQ5FWZ3XPHHEB","short_pith_number":"pith:M2A5OJJS","canonical_record":{"source":{"id":"2605.27260","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-05-26T16:37:40Z","cross_cats_sorted":["math-ph","math.AP","math.MP"],"title_canon_sha256":"1200ebefd18f294e67301d63b4368c815a7ab094f2256fe74fc9811b0deeca1c","abstract_canon_sha256":"3633b14b10d6dc6be197abf192cf99b4e5141883bf1eb412971f1a627055e0ca"},"schema_version":"1.0"},"canonical_sha256":"6681d7253293e6dd4e1d2db3bbbce7205e92b6f745862aaf4fef2f1a463f918f","source":{"kind":"arxiv","id":"2605.27260","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.27260","created_at":"2026-05-27T02:06:08Z"},{"alias_kind":"arxiv_version","alias_value":"2605.27260v1","created_at":"2026-05-27T02:06:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.27260","created_at":"2026-05-27T02:06:08Z"},{"alias_kind":"pith_short_12","alias_value":"M2A5OJJSSPTN","created_at":"2026-05-27T02:06:08Z"},{"alias_kind":"pith_short_16","alias_value":"M2A5OJJSSPTN2TQ5","created_at":"2026-05-27T02:06:08Z"},{"alias_kind":"pith_short_8","alias_value":"M2A5OJJS","created_at":"2026-05-27T02:06:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:M2A5OJJSSPTN2TQ5FWZ3XPHHEB","target":"record","payload":{"canonical_record":{"source":{"id":"2605.27260","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-05-26T16:37:40Z","cross_cats_sorted":["math-ph","math.AP","math.MP"],"title_canon_sha256":"1200ebefd18f294e67301d63b4368c815a7ab094f2256fe74fc9811b0deeca1c","abstract_canon_sha256":"3633b14b10d6dc6be197abf192cf99b4e5141883bf1eb412971f1a627055e0ca"},"schema_version":"1.0"},"canonical_sha256":"6681d7253293e6dd4e1d2db3bbbce7205e92b6f745862aaf4fef2f1a463f918f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-27T02:06:08.800758Z","signature_b64":"B5SlWiEmdca6IZ57jPYd9hT3yQtuTKlYM0V7l85gO9RHpaUHdfnIj/l1JWPDJ1WzyfBjSK6zq7ddeYRjqzDoAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6681d7253293e6dd4e1d2db3bbbce7205e92b6f745862aaf4fef2f1a463f918f","last_reissued_at":"2026-05-27T02:06:08.800033Z","signature_status":"signed_v1","first_computed_at":"2026-05-27T02:06:08.800033Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.27260","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":"2026-05-27T02:06:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L/7XNW/oS3kk1ZmjcqOZpYWvtwIADXf5ZdQeUuzuZSul5GTgslsmGy/35yrTbcDF9r4vRdX8uvwCMZSr6ECJBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T12:02:33.646194Z"},"content_sha256":"defe6b31cf5fc4ade729133b5b0d058d74b45997ff1aa1ee4ac9b7d3349a9c14","schema_version":"1.0","event_id":"sha256:defe6b31cf5fc4ade729133b5b0d058d74b45997ff1aa1ee4ac9b7d3349a9c14"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:M2A5OJJSSPTN2TQ5FWZ3XPHHEB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Practical tensor calculus on embedded submanifolds of arbitrary codimension","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.DG","authors_text":"Vladimir Yushutin","submitted_at":"2026-05-26T16:37:40Z","abstract_excerpt":"We present a fully extrinsic, parametrization-free variant of tensor calculus on embedded, possibly evolving, submanifolds with boundary in arbitrary dimension and codimension. The proposed approach is component-free and, for general rank tensors, covers fundamental concepts such as tangential projection, extrinsic and covariant derivatives, the extrinsic Stokes' formula, and the Laplace-Beltrami operator. The distinctive features of the developed framework are its algorithmic recursivity and the transparency provided by the special row representation of tensors reminiscent of the recursive da"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.27260","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/2605.27260/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":"2026-05-27T02:06:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/T1mgAMgpmblJ+vItWczObEFIA/KpjmfhJrKsWkx4lFkUVOBFMDtKmus8OHRAGFhMEjLvSojDy4sZjCiMyeRDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T12:02:33.646963Z"},"content_sha256":"12c023b35cf8221c5a91f567195d15ec63a8635533b0016f8b0f8615c84050bc","schema_version":"1.0","event_id":"sha256:12c023b35cf8221c5a91f567195d15ec63a8635533b0016f8b0f8615c84050bc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M2A5OJJSSPTN2TQ5FWZ3XPHHEB/bundle.json","state_url":"https://pith.science/pith/M2A5OJJSSPTN2TQ5FWZ3XPHHEB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M2A5OJJSSPTN2TQ5FWZ3XPHHEB/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":"2026-06-09T12:02:33Z","links":{"resolver":"https://pith.science/pith/M2A5OJJSSPTN2TQ5FWZ3XPHHEB","bundle":"https://pith.science/pith/M2A5OJJSSPTN2TQ5FWZ3XPHHEB/bundle.json","state":"https://pith.science/pith/M2A5OJJSSPTN2TQ5FWZ3XPHHEB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M2A5OJJSSPTN2TQ5FWZ3XPHHEB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:M2A5OJJSSPTN2TQ5FWZ3XPHHEB","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":"3633b14b10d6dc6be197abf192cf99b4e5141883bf1eb412971f1a627055e0ca","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-05-26T16:37:40Z","title_canon_sha256":"1200ebefd18f294e67301d63b4368c815a7ab094f2256fe74fc9811b0deeca1c"},"schema_version":"1.0","source":{"id":"2605.27260","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.27260","created_at":"2026-05-27T02:06:08Z"},{"alias_kind":"arxiv_version","alias_value":"2605.27260v1","created_at":"2026-05-27T02:06:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.27260","created_at":"2026-05-27T02:06:08Z"},{"alias_kind":"pith_short_12","alias_value":"M2A5OJJSSPTN","created_at":"2026-05-27T02:06:08Z"},{"alias_kind":"pith_short_16","alias_value":"M2A5OJJSSPTN2TQ5","created_at":"2026-05-27T02:06:08Z"},{"alias_kind":"pith_short_8","alias_value":"M2A5OJJS","created_at":"2026-05-27T02:06:08Z"}],"graph_snapshots":[{"event_id":"sha256:12c023b35cf8221c5a91f567195d15ec63a8635533b0016f8b0f8615c84050bc","target":"graph","created_at":"2026-05-27T02:06:08Z","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/2605.27260/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a fully extrinsic, parametrization-free variant of tensor calculus on embedded, possibly evolving, submanifolds with boundary in arbitrary dimension and codimension. The proposed approach is component-free and, for general rank tensors, covers fundamental concepts such as tangential projection, extrinsic and covariant derivatives, the extrinsic Stokes' formula, and the Laplace-Beltrami operator. The distinctive features of the developed framework are its algorithmic recursivity and the transparency provided by the special row representation of tensors reminiscent of the recursive da","authors_text":"Vladimir Yushutin","cross_cats":["math-ph","math.AP","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-05-26T16:37:40Z","title":"Practical tensor calculus on embedded submanifolds of arbitrary codimension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.27260","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:defe6b31cf5fc4ade729133b5b0d058d74b45997ff1aa1ee4ac9b7d3349a9c14","target":"record","created_at":"2026-05-27T02:06:08Z","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":"3633b14b10d6dc6be197abf192cf99b4e5141883bf1eb412971f1a627055e0ca","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-05-26T16:37:40Z","title_canon_sha256":"1200ebefd18f294e67301d63b4368c815a7ab094f2256fe74fc9811b0deeca1c"},"schema_version":"1.0","source":{"id":"2605.27260","kind":"arxiv","version":1}},"canonical_sha256":"6681d7253293e6dd4e1d2db3bbbce7205e92b6f745862aaf4fef2f1a463f918f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6681d7253293e6dd4e1d2db3bbbce7205e92b6f745862aaf4fef2f1a463f918f","first_computed_at":"2026-05-27T02:06:08.800033Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-27T02:06:08.800033Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B5SlWiEmdca6IZ57jPYd9hT3yQtuTKlYM0V7l85gO9RHpaUHdfnIj/l1JWPDJ1WzyfBjSK6zq7ddeYRjqzDoAw==","signature_status":"signed_v1","signed_at":"2026-05-27T02:06:08.800758Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.27260","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:defe6b31cf5fc4ade729133b5b0d058d74b45997ff1aa1ee4ac9b7d3349a9c14","sha256:12c023b35cf8221c5a91f567195d15ec63a8635533b0016f8b0f8615c84050bc"],"state_sha256":"2effae342fa3f2e7f419bd3e24b7485633ef2dca355e5d8ec4fc63be70becf95"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CdAHuumtMsFm43+Bb9J7DxY37AnSEFIOVxrNEsLV28nCjTNO5Py6qUdW0sKZ60Sk2rCmNNS2KGIWPPQjm8KoCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T12:02:33.651810Z","bundle_sha256":"474564e38ab213e462ba11c04e346461c7ba4d90c28c03047bf3473706987f5f"}}