{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:2FFCNGTE7MLPRNNH2Y6MOZQL3S","short_pith_number":"pith:2FFCNGTE","canonical_record":{"source":{"id":"2506.08869","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2025-06-10T15:01:37Z","cross_cats_sorted":["math.DG","math.MP"],"title_canon_sha256":"014923361049af548a2143c93b0043f0571d0c56da3f3fb6297021dca60dfed4","abstract_canon_sha256":"7fad1670bfebc753cdcb94889a48c38853c55a5dadbe96ffa058bb782b041b32"},"schema_version":"1.0"},"canonical_sha256":"d14a269a64fb16f8b5a7d63cc7660bdcb2706fd128fc1bb9e6d039ce1d2f3915","source":{"kind":"arxiv","id":"2506.08869","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.08869","created_at":"2026-07-05T11:21:49Z"},{"alias_kind":"arxiv_version","alias_value":"2506.08869v3","created_at":"2026-07-05T11:21:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.08869","created_at":"2026-07-05T11:21:49Z"},{"alias_kind":"pith_short_12","alias_value":"2FFCNGTE7MLP","created_at":"2026-07-05T11:21:49Z"},{"alias_kind":"pith_short_16","alias_value":"2FFCNGTE7MLPRNNH","created_at":"2026-07-05T11:21:49Z"},{"alias_kind":"pith_short_8","alias_value":"2FFCNGTE","created_at":"2026-07-05T11:21:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:2FFCNGTE7MLPRNNH2Y6MOZQL3S","target":"record","payload":{"canonical_record":{"source":{"id":"2506.08869","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2025-06-10T15:01:37Z","cross_cats_sorted":["math.DG","math.MP"],"title_canon_sha256":"014923361049af548a2143c93b0043f0571d0c56da3f3fb6297021dca60dfed4","abstract_canon_sha256":"7fad1670bfebc753cdcb94889a48c38853c55a5dadbe96ffa058bb782b041b32"},"schema_version":"1.0"},"canonical_sha256":"d14a269a64fb16f8b5a7d63cc7660bdcb2706fd128fc1bb9e6d039ce1d2f3915","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:21:49.071026Z","signature_b64":"9eA27cqBwPx0aKpGf0AdV1xb1aJTnsUIkdXI121VjFoLv/UXwvtTQ+BnIh30ZawbdRFOf5TQjl9EgfqN1gKHBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d14a269a64fb16f8b5a7d63cc7660bdcb2706fd128fc1bb9e6d039ce1d2f3915","last_reissued_at":"2026-07-05T11:21:49.070545Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:21:49.070545Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.08869","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":"2026-07-05T11:21:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"odZywEs9BmESWS4pUxR6/jPJ7HWngWZj/PHUPxNwKyoEW1OaDiKgtJ0WTrv/KL0tsqqPQd+zgCsGXMi6CnonCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T16:52:33.202922Z"},"content_sha256":"3c5f8d7167f0f965aa56ff8060687cd4898995da1a3844030d5e993fbafcdcb0","schema_version":"1.0","event_id":"sha256:3c5f8d7167f0f965aa56ff8060687cd4898995da1a3844030d5e993fbafcdcb0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:2FFCNGTE7MLPRNNH2Y6MOZQL3S","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convergence of Normal Form Power Series for Infinite-Dimensional Lie Pseudo-Group Actions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DG","math.MP"],"primary_cat":"math-ph","authors_text":"Francis Valiquette, Masoud Sabzevari, Peter J. Olver","submitted_at":"2025-06-10T15:01:37Z","abstract_excerpt":"We prove the convergence of normal form power series for suitably nonsingular analytic submanifolds under a broad class of infinite-dimensional Lie pseudo-group actions. Our theorem is illustrated by a number of examples, and includes, as a particular case, Chern and Moser's celebrated convergence theorem for normal forms of real hypersurfaces. The construction of normal forms relies on the equivariant moving frame method, while the convergence proof is based on the realization that the normal form can be recovered as part of the solution to an initial value problem for an involutive system of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.08869","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/2506.08869/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":"2026-07-05T11:21:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g9jUYikx6h+QepoNfhPT8IzIrlFyJ3MNWXOlabS8tKgMThtOH5iTssnKN3P9Z+Lm4Ju4RNg0JVsEWlX9kOV2Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T16:52:33.203439Z"},"content_sha256":"78c118c8c6e5c4ec3297efc1418f57b4732867000ea11ada194b7a274adec62a","schema_version":"1.0","event_id":"sha256:78c118c8c6e5c4ec3297efc1418f57b4732867000ea11ada194b7a274adec62a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2FFCNGTE7MLPRNNH2Y6MOZQL3S/bundle.json","state_url":"https://pith.science/pith/2FFCNGTE7MLPRNNH2Y6MOZQL3S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2FFCNGTE7MLPRNNH2Y6MOZQL3S/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":"2026-08-08T16:52:33Z","links":{"resolver":"https://pith.science/pith/2FFCNGTE7MLPRNNH2Y6MOZQL3S","bundle":"https://pith.science/pith/2FFCNGTE7MLPRNNH2Y6MOZQL3S/bundle.json","state":"https://pith.science/pith/2FFCNGTE7MLPRNNH2Y6MOZQL3S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2FFCNGTE7MLPRNNH2Y6MOZQL3S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:2FFCNGTE7MLPRNNH2Y6MOZQL3S","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":"7fad1670bfebc753cdcb94889a48c38853c55a5dadbe96ffa058bb782b041b32","cross_cats_sorted":["math.DG","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2025-06-10T15:01:37Z","title_canon_sha256":"014923361049af548a2143c93b0043f0571d0c56da3f3fb6297021dca60dfed4"},"schema_version":"1.0","source":{"id":"2506.08869","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.08869","created_at":"2026-07-05T11:21:49Z"},{"alias_kind":"arxiv_version","alias_value":"2506.08869v3","created_at":"2026-07-05T11:21:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.08869","created_at":"2026-07-05T11:21:49Z"},{"alias_kind":"pith_short_12","alias_value":"2FFCNGTE7MLP","created_at":"2026-07-05T11:21:49Z"},{"alias_kind":"pith_short_16","alias_value":"2FFCNGTE7MLPRNNH","created_at":"2026-07-05T11:21:49Z"},{"alias_kind":"pith_short_8","alias_value":"2FFCNGTE","created_at":"2026-07-05T11:21:49Z"}],"graph_snapshots":[{"event_id":"sha256:78c118c8c6e5c4ec3297efc1418f57b4732867000ea11ada194b7a274adec62a","target":"graph","created_at":"2026-07-05T11:21:49Z","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/2506.08869/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove the convergence of normal form power series for suitably nonsingular analytic submanifolds under a broad class of infinite-dimensional Lie pseudo-group actions. Our theorem is illustrated by a number of examples, and includes, as a particular case, Chern and Moser's celebrated convergence theorem for normal forms of real hypersurfaces. The construction of normal forms relies on the equivariant moving frame method, while the convergence proof is based on the realization that the normal form can be recovered as part of the solution to an initial value problem for an involutive system of","authors_text":"Francis Valiquette, Masoud Sabzevari, Peter J. Olver","cross_cats":["math.DG","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2025-06-10T15:01:37Z","title":"Convergence of Normal Form Power Series for Infinite-Dimensional Lie Pseudo-Group Actions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.08869","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":"sha256:3c5f8d7167f0f965aa56ff8060687cd4898995da1a3844030d5e993fbafcdcb0","target":"record","created_at":"2026-07-05T11:21:49Z","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":"7fad1670bfebc753cdcb94889a48c38853c55a5dadbe96ffa058bb782b041b32","cross_cats_sorted":["math.DG","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2025-06-10T15:01:37Z","title_canon_sha256":"014923361049af548a2143c93b0043f0571d0c56da3f3fb6297021dca60dfed4"},"schema_version":"1.0","source":{"id":"2506.08869","kind":"arxiv","version":3}},"canonical_sha256":"d14a269a64fb16f8b5a7d63cc7660bdcb2706fd128fc1bb9e6d039ce1d2f3915","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d14a269a64fb16f8b5a7d63cc7660bdcb2706fd128fc1bb9e6d039ce1d2f3915","first_computed_at":"2026-07-05T11:21:49.070545Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:21:49.070545Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9eA27cqBwPx0aKpGf0AdV1xb1aJTnsUIkdXI121VjFoLv/UXwvtTQ+BnIh30ZawbdRFOf5TQjl9EgfqN1gKHBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:21:49.071026Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.08869","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3c5f8d7167f0f965aa56ff8060687cd4898995da1a3844030d5e993fbafcdcb0","sha256:78c118c8c6e5c4ec3297efc1418f57b4732867000ea11ada194b7a274adec62a"],"state_sha256":"2938723aa284eec4fde666efe24ad9abb492f9f5d094be50922ae098332bcd53"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lXRJmTEqooGJFkr9mUxoRKL0KLqqvV/fgEivw8XpqlCBAlFgME/Z8knBYpim7O1vs3KQX4v9KxkIArKObRJJAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T16:52:33.208833Z","bundle_sha256":"f1e73d17b0b489afb0be36d73be4b196cc0d5f264a99eeb6d30776ea6765c0f3"}}