{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:SFRKK6PTGEXENQUTVMZOWBYKSD","short_pith_number":"pith:SFRKK6PT","canonical_record":{"source":{"id":"1912.00676","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-12-02T10:39:20Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"9dc95cfa83e10b0c0fdf8e6d3f4edcfd6a818c6c0019e9766e074b9f0a7fd2dd","abstract_canon_sha256":"18a13e278e59810b99eca426d72052b0381b8a537e4cad011eb93e389ea3e15b"},"schema_version":"1.0"},"canonical_sha256":"9162a579f3312e46c293ab32eb070a90ddcc54c739c0c042a29d96044bc7c3b9","source":{"kind":"arxiv","id":"1912.00676","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1912.00676","created_at":"2026-07-05T03:49:06Z"},{"alias_kind":"arxiv_version","alias_value":"1912.00676v3","created_at":"2026-07-05T03:49:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1912.00676","created_at":"2026-07-05T03:49:06Z"},{"alias_kind":"pith_short_12","alias_value":"SFRKK6PTGEXE","created_at":"2026-07-05T03:49:06Z"},{"alias_kind":"pith_short_16","alias_value":"SFRKK6PTGEXENQUT","created_at":"2026-07-05T03:49:06Z"},{"alias_kind":"pith_short_8","alias_value":"SFRKK6PT","created_at":"2026-07-05T03:49:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:SFRKK6PTGEXENQUTVMZOWBYKSD","target":"record","payload":{"canonical_record":{"source":{"id":"1912.00676","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-12-02T10:39:20Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"9dc95cfa83e10b0c0fdf8e6d3f4edcfd6a818c6c0019e9766e074b9f0a7fd2dd","abstract_canon_sha256":"18a13e278e59810b99eca426d72052b0381b8a537e4cad011eb93e389ea3e15b"},"schema_version":"1.0"},"canonical_sha256":"9162a579f3312e46c293ab32eb070a90ddcc54c739c0c042a29d96044bc7c3b9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:49:06.831275Z","signature_b64":"oe6IVFc1elett7IsSNB3IvsRPfq9U3C22GYehUanIi/9X3WjjAUtdR1ic9BYaCxtGfYoAFfda+WmuxmHNTJWAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9162a579f3312e46c293ab32eb070a90ddcc54c739c0c042a29d96044bc7c3b9","last_reissued_at":"2026-07-05T03:49:06.830922Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:49:06.830922Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1912.00676","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":"2026-07-05T03:49:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sDv35GKEv42hLokHXSSos7vFITg/8JWmDtHBXLv63JJ3Lgy2h8OtHS7f5KepuIPDXQ8Kl1w/c56GaOjSfQRkBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T10:48:12.820896Z"},"content_sha256":"ef769a65a0e84655ebe52f3af39a2d4cadabe45d39db80dd69a15ab3f80969b1","schema_version":"1.0","event_id":"sha256:ef769a65a0e84655ebe52f3af39a2d4cadabe45d39db80dd69a15ab3f80969b1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:SFRKK6PTGEXENQUTVMZOWBYKSD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Differential Geometric Formulations of Slow Invariant Manifold Computation: Geodesic Stretching and Flow Curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.DS","authors_text":"Dirk Lebiedz, Johannes Poppe","submitted_at":"2019-12-02T10:39:20Z","abstract_excerpt":"The theory of slow invariant manifolds (SIMs) is the foundation of various model-order reduction techniques for dissipative dynamical systems with multiple time-scales, e.g. in chemical kinetic models. The construction of SIMs and many approximation methods exploit the restrictive requirement of an explicit time-scale separation parameter. Most of those methods are also not formulated covariantly, i.e. in terms of tensorial constructions. We propose an intrinsically coordinate-free differential geometric approximation criterion approximating normally attracting invariant manifolds (NAIMs). We "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.00676","kind":"arxiv","version":3},"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/1912.00676/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":"2026-07-05T03:49:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dYlYEdx9V6VlZfU1sd3EhTh0YDveSffOTcbitc08BIqP1lhDXAxKA9bzlHG1RN5F61oXlw6aWqii40x43oC2Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T10:48:12.821271Z"},"content_sha256":"dc59bafa1d9578b1b1ff537e1194bf9bb4739e05080a069c84f9a83377c04063","schema_version":"1.0","event_id":"sha256:dc59bafa1d9578b1b1ff537e1194bf9bb4739e05080a069c84f9a83377c04063"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SFRKK6PTGEXENQUTVMZOWBYKSD/bundle.json","state_url":"https://pith.science/pith/SFRKK6PTGEXENQUTVMZOWBYKSD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SFRKK6PTGEXENQUTVMZOWBYKSD/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":"2026-07-06T10:48:12Z","links":{"resolver":"https://pith.science/pith/SFRKK6PTGEXENQUTVMZOWBYKSD","bundle":"https://pith.science/pith/SFRKK6PTGEXENQUTVMZOWBYKSD/bundle.json","state":"https://pith.science/pith/SFRKK6PTGEXENQUTVMZOWBYKSD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SFRKK6PTGEXENQUTVMZOWBYKSD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:SFRKK6PTGEXENQUTVMZOWBYKSD","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":"18a13e278e59810b99eca426d72052b0381b8a537e4cad011eb93e389ea3e15b","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-12-02T10:39:20Z","title_canon_sha256":"9dc95cfa83e10b0c0fdf8e6d3f4edcfd6a818c6c0019e9766e074b9f0a7fd2dd"},"schema_version":"1.0","source":{"id":"1912.00676","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1912.00676","created_at":"2026-07-05T03:49:06Z"},{"alias_kind":"arxiv_version","alias_value":"1912.00676v3","created_at":"2026-07-05T03:49:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1912.00676","created_at":"2026-07-05T03:49:06Z"},{"alias_kind":"pith_short_12","alias_value":"SFRKK6PTGEXE","created_at":"2026-07-05T03:49:06Z"},{"alias_kind":"pith_short_16","alias_value":"SFRKK6PTGEXENQUT","created_at":"2026-07-05T03:49:06Z"},{"alias_kind":"pith_short_8","alias_value":"SFRKK6PT","created_at":"2026-07-05T03:49:06Z"}],"graph_snapshots":[{"event_id":"sha256:dc59bafa1d9578b1b1ff537e1194bf9bb4739e05080a069c84f9a83377c04063","target":"graph","created_at":"2026-07-05T03:49:06Z","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/1912.00676/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The theory of slow invariant manifolds (SIMs) is the foundation of various model-order reduction techniques for dissipative dynamical systems with multiple time-scales, e.g. in chemical kinetic models. The construction of SIMs and many approximation methods exploit the restrictive requirement of an explicit time-scale separation parameter. Most of those methods are also not formulated covariantly, i.e. in terms of tensorial constructions. We propose an intrinsically coordinate-free differential geometric approximation criterion approximating normally attracting invariant manifolds (NAIMs). We ","authors_text":"Dirk Lebiedz, Johannes Poppe","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-12-02T10:39:20Z","title":"On Differential Geometric Formulations of Slow Invariant Manifold Computation: Geodesic Stretching and Flow Curvature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.00676","kind":"arxiv","version":3},"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:ef769a65a0e84655ebe52f3af39a2d4cadabe45d39db80dd69a15ab3f80969b1","target":"record","created_at":"2026-07-05T03:49:06Z","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":"18a13e278e59810b99eca426d72052b0381b8a537e4cad011eb93e389ea3e15b","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-12-02T10:39:20Z","title_canon_sha256":"9dc95cfa83e10b0c0fdf8e6d3f4edcfd6a818c6c0019e9766e074b9f0a7fd2dd"},"schema_version":"1.0","source":{"id":"1912.00676","kind":"arxiv","version":3}},"canonical_sha256":"9162a579f3312e46c293ab32eb070a90ddcc54c739c0c042a29d96044bc7c3b9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9162a579f3312e46c293ab32eb070a90ddcc54c739c0c042a29d96044bc7c3b9","first_computed_at":"2026-07-05T03:49:06.830922Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:49:06.830922Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oe6IVFc1elett7IsSNB3IvsRPfq9U3C22GYehUanIi/9X3WjjAUtdR1ic9BYaCxtGfYoAFfda+WmuxmHNTJWAA==","signature_status":"signed_v1","signed_at":"2026-07-05T03:49:06.831275Z","signed_message":"canonical_sha256_bytes"},"source_id":"1912.00676","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ef769a65a0e84655ebe52f3af39a2d4cadabe45d39db80dd69a15ab3f80969b1","sha256:dc59bafa1d9578b1b1ff537e1194bf9bb4739e05080a069c84f9a83377c04063"],"state_sha256":"dda5e9d233f422b4a150f1b59399f905d6021393059bc244af6efc56032295a9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Two1Kfkm2XvmcorWQbqB5kZJNY9cMriRYevpx8sVAPz99Wq/Ow5DUMIwRgIDZi41IlSvOguW0FZzSvJdEfENDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T10:48:12.823212Z","bundle_sha256":"7b95ea2251d688e86065b6d6e821fe77de5278d9db20334b1646689b8ab97c4f"}}