{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:PTMWHUN7S6NP4L56TVDJWLQIDK","short_pith_number":"pith:PTMWHUN7","canonical_record":{"source":{"id":"2406.16642","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2024-06-24T13:46:58Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"bfa6798bab1242538cba6a0b65c29da9c8e4e604a587ac5358947c768828b655","abstract_canon_sha256":"723e30e474fd2951a155494cce4662d74246b0b033148ac6f07eb18e6c67622e"},"schema_version":"1.0"},"canonical_sha256":"7cd963d1bf979afe2fbe9d469b2e081a977fb448dc13c8d478618facf404f27d","source":{"kind":"arxiv","id":"2406.16642","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.16642","created_at":"2026-07-05T08:36:01Z"},{"alias_kind":"arxiv_version","alias_value":"2406.16642v1","created_at":"2026-07-05T08:36:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.16642","created_at":"2026-07-05T08:36:01Z"},{"alias_kind":"pith_short_12","alias_value":"PTMWHUN7S6NP","created_at":"2026-07-05T08:36:01Z"},{"alias_kind":"pith_short_16","alias_value":"PTMWHUN7S6NP4L56","created_at":"2026-07-05T08:36:01Z"},{"alias_kind":"pith_short_8","alias_value":"PTMWHUN7","created_at":"2026-07-05T08:36:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:PTMWHUN7S6NP4L56TVDJWLQIDK","target":"record","payload":{"canonical_record":{"source":{"id":"2406.16642","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2024-06-24T13:46:58Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"bfa6798bab1242538cba6a0b65c29da9c8e4e604a587ac5358947c768828b655","abstract_canon_sha256":"723e30e474fd2951a155494cce4662d74246b0b033148ac6f07eb18e6c67622e"},"schema_version":"1.0"},"canonical_sha256":"7cd963d1bf979afe2fbe9d469b2e081a977fb448dc13c8d478618facf404f27d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:36:01.763173Z","signature_b64":"sRkrNTlddUjuTJ3TZeIO0zs8oIdVGHfDGC2pFFFVmebJmD4g1xzdcRCmjOCd8oZg604BW8+GX4Qx2Z8OdhBmAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7cd963d1bf979afe2fbe9d469b2e081a977fb448dc13c8d478618facf404f27d","last_reissued_at":"2026-07-05T08:36:01.762662Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:36:01.762662Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2406.16642","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":"2026-07-05T08:36:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GQs1wS7rqWdyVY/bh1KFLI1BjBc9BhyLtFWaeYFHisqmVbyyBb4mxJK5PksEFW8GPhjZPR0KNBA0Y3n6fensCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T07:44:11.550559Z"},"content_sha256":"343c8b1eebeab6223187e4769494e6c43ab84f24bf6aa06e8f74179b013f31f5","schema_version":"1.0","event_id":"sha256:343c8b1eebeab6223187e4769494e6c43ab84f24bf6aa06e8f74179b013f31f5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:PTMWHUN7S6NP4L56TVDJWLQIDK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Noncommutative orbital stability of stochastic patterns in Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DS","authors_text":"Joris van Winden","submitted_at":"2024-06-24T13:46:58Z","abstract_excerpt":"We consider stochastic perturbations of PDEs which have special pattern solutions, such as (nonlinear) travelling waves, solitons, and spiral waves. We show orbital stability of these patterns on a timescale which is exponential in the inverse square of the noise amplitude. We systematically treat equations with noncommutative symmetry groups, and show how the noncommutativity affects the motion of the pattern. This is done by introducing a new method to track the (generalized) phase of the pattern. Furthermore, we demonstrate how orbital stability arises from a mismatch of symmetry between th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.16642","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/2406.16642/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":"2026-07-05T08:36:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+SqDnuKW3pP14AC//LzF9acAPLPwSTXDI0o/SgjsCYQXUCic0TKEnpmsnVfePgXrBHBp2WGHgKOt7PriABWmDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T07:44:11.551342Z"},"content_sha256":"7743925993f7d1706393dc966053342de2c543ba2874f9705fbbf8661dff2706","schema_version":"1.0","event_id":"sha256:7743925993f7d1706393dc966053342de2c543ba2874f9705fbbf8661dff2706"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PTMWHUN7S6NP4L56TVDJWLQIDK/bundle.json","state_url":"https://pith.science/pith/PTMWHUN7S6NP4L56TVDJWLQIDK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PTMWHUN7S6NP4L56TVDJWLQIDK/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":"2026-08-12T07:44:11Z","links":{"resolver":"https://pith.science/pith/PTMWHUN7S6NP4L56TVDJWLQIDK","bundle":"https://pith.science/pith/PTMWHUN7S6NP4L56TVDJWLQIDK/bundle.json","state":"https://pith.science/pith/PTMWHUN7S6NP4L56TVDJWLQIDK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PTMWHUN7S6NP4L56TVDJWLQIDK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:PTMWHUN7S6NP4L56TVDJWLQIDK","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":"723e30e474fd2951a155494cce4662d74246b0b033148ac6f07eb18e6c67622e","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2024-06-24T13:46:58Z","title_canon_sha256":"bfa6798bab1242538cba6a0b65c29da9c8e4e604a587ac5358947c768828b655"},"schema_version":"1.0","source":{"id":"2406.16642","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.16642","created_at":"2026-07-05T08:36:01Z"},{"alias_kind":"arxiv_version","alias_value":"2406.16642v1","created_at":"2026-07-05T08:36:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.16642","created_at":"2026-07-05T08:36:01Z"},{"alias_kind":"pith_short_12","alias_value":"PTMWHUN7S6NP","created_at":"2026-07-05T08:36:01Z"},{"alias_kind":"pith_short_16","alias_value":"PTMWHUN7S6NP4L56","created_at":"2026-07-05T08:36:01Z"},{"alias_kind":"pith_short_8","alias_value":"PTMWHUN7","created_at":"2026-07-05T08:36:01Z"}],"graph_snapshots":[{"event_id":"sha256:7743925993f7d1706393dc966053342de2c543ba2874f9705fbbf8661dff2706","target":"graph","created_at":"2026-07-05T08:36:01Z","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/2406.16642/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider stochastic perturbations of PDEs which have special pattern solutions, such as (nonlinear) travelling waves, solitons, and spiral waves. We show orbital stability of these patterns on a timescale which is exponential in the inverse square of the noise amplitude. We systematically treat equations with noncommutative symmetry groups, and show how the noncommutativity affects the motion of the pattern. This is done by introducing a new method to track the (generalized) phase of the pattern. Furthermore, we demonstrate how orbital stability arises from a mismatch of symmetry between th","authors_text":"Joris van Winden","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2024-06-24T13:46:58Z","title":"Noncommutative orbital stability of stochastic patterns in Banach spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.16642","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":"sha256:343c8b1eebeab6223187e4769494e6c43ab84f24bf6aa06e8f74179b013f31f5","target":"record","created_at":"2026-07-05T08:36:01Z","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":"723e30e474fd2951a155494cce4662d74246b0b033148ac6f07eb18e6c67622e","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2024-06-24T13:46:58Z","title_canon_sha256":"bfa6798bab1242538cba6a0b65c29da9c8e4e604a587ac5358947c768828b655"},"schema_version":"1.0","source":{"id":"2406.16642","kind":"arxiv","version":1}},"canonical_sha256":"7cd963d1bf979afe2fbe9d469b2e081a977fb448dc13c8d478618facf404f27d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7cd963d1bf979afe2fbe9d469b2e081a977fb448dc13c8d478618facf404f27d","first_computed_at":"2026-07-05T08:36:01.762662Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:36:01.762662Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sRkrNTlddUjuTJ3TZeIO0zs8oIdVGHfDGC2pFFFVmebJmD4g1xzdcRCmjOCd8oZg604BW8+GX4Qx2Z8OdhBmAw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:36:01.763173Z","signed_message":"canonical_sha256_bytes"},"source_id":"2406.16642","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:343c8b1eebeab6223187e4769494e6c43ab84f24bf6aa06e8f74179b013f31f5","sha256:7743925993f7d1706393dc966053342de2c543ba2874f9705fbbf8661dff2706"],"state_sha256":"d4a235154761015bccbf29c87185f6b4f20e6400fb78a079242f587c92f0c048"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AgySHI85L8qJaRj4O1egKhkffOtbaai6zAcBZrzfxhxj0dx6ideC6DLP3TwfKhem6lNdbV8YROQjE1B1zy0TAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T07:44:11.559476Z","bundle_sha256":"2c899a739ea62d8c37dfb6dd84fa9544cc48cd3feeb7ad3df4bd21d6a4afe397"}}