{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:ESRK7F3LJNLBIB7MBIJ3J2JJKN","short_pith_number":"pith:ESRK7F3L","canonical_record":{"source":{"id":"1010.2342","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-10-12T09:59:19Z","cross_cats_sorted":[],"title_canon_sha256":"c46cfc7e43490b4fd3fd702a3d4a93464fae070b40de68400187a00521ffa5fc","abstract_canon_sha256":"535c75e03fee86c7b23fff462c181e697adaa078bd1ab6df1a262a3e6db23080"},"schema_version":"1.0"},"canonical_sha256":"24a2af976b4b561407ec0a13b4e92953599fc738229c3fc098279356cfcb07bf","source":{"kind":"arxiv","id":"1010.2342","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.2342","created_at":"2026-05-18T03:00:59Z"},{"alias_kind":"arxiv_version","alias_value":"1010.2342v3","created_at":"2026-05-18T03:00:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.2342","created_at":"2026-05-18T03:00:59Z"},{"alias_kind":"pith_short_12","alias_value":"ESRK7F3LJNLB","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"ESRK7F3LJNLBIB7M","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"ESRK7F3L","created_at":"2026-05-18T12:26:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:ESRK7F3LJNLBIB7MBIJ3J2JJKN","target":"record","payload":{"canonical_record":{"source":{"id":"1010.2342","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-10-12T09:59:19Z","cross_cats_sorted":[],"title_canon_sha256":"c46cfc7e43490b4fd3fd702a3d4a93464fae070b40de68400187a00521ffa5fc","abstract_canon_sha256":"535c75e03fee86c7b23fff462c181e697adaa078bd1ab6df1a262a3e6db23080"},"schema_version":"1.0"},"canonical_sha256":"24a2af976b4b561407ec0a13b4e92953599fc738229c3fc098279356cfcb07bf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:00:59.673792Z","signature_b64":"vU7Eh/EfY+FVdfVQimj7VsHYvOCffCRw4704FxN9xQvshHLNQ+GGV8X73xWl8CR9U10ct4OVJ+/riCw6Gc2sDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"24a2af976b4b561407ec0a13b4e92953599fc738229c3fc098279356cfcb07bf","last_reissued_at":"2026-05-18T03:00:59.672999Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:00:59.672999Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1010.2342","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":"2026-05-18T03:00:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OInSm8IVhf68Y689p3lFz7kBH3TSLLDga2gmQcBRYyYvmAopKSEkpDLXxZVep/eYjxMt4KkSZaU5CI5j8NSeCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T20:49:02.370282Z"},"content_sha256":"324fe2ac899f402290d1773d33fee1c95fa6caa71717d0ed8e1f073c98b3c147","schema_version":"1.0","event_id":"sha256:324fe2ac899f402290d1773d33fee1c95fa6caa71717d0ed8e1f073c98b3c147"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:ESRK7F3LJNLBIB7MBIJ3J2JJKN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fourier transform and rigidity of certain distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Binyong Sun, Chen-bo Zhu","submitted_at":"2010-10-12T09:59:19Z","abstract_excerpt":"Let $E$ be a finite dimensional vector space over a local field, and $F$ be its dual. For a closed subset $X$ of $E$, and $Y$ of $F$, consider the space $D^{-\\xi}(E;X,Y)$ of tempered distributions on $E$ whose support are contained in $X$ and support of whose Fourier transform are contained in $Y$. We show that $D^{-\\xi}(E;X,Y)$ possesses a certain rigidity property, for $X$, $Y$ which are some finite unions of affine subspaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.2342","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":""},"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":"2026-05-18T03:00:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2YN63cLpVTBZQUqVHxyjIdZ6ZupAmcEExOgRLIsdE9pbJbuUKI/Flg6+JoyY38YPGL63lxYQvMga7P1PTwg8CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T20:49:02.370755Z"},"content_sha256":"67f9cf02c52c5949b7daf1f2dae90664433b43378dbdb3f03611602d9b58a223","schema_version":"1.0","event_id":"sha256:67f9cf02c52c5949b7daf1f2dae90664433b43378dbdb3f03611602d9b58a223"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ESRK7F3LJNLBIB7MBIJ3J2JJKN/bundle.json","state_url":"https://pith.science/pith/ESRK7F3LJNLBIB7MBIJ3J2JJKN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ESRK7F3LJNLBIB7MBIJ3J2JJKN/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":"2026-06-24T20:49:02Z","links":{"resolver":"https://pith.science/pith/ESRK7F3LJNLBIB7MBIJ3J2JJKN","bundle":"https://pith.science/pith/ESRK7F3LJNLBIB7MBIJ3J2JJKN/bundle.json","state":"https://pith.science/pith/ESRK7F3LJNLBIB7MBIJ3J2JJKN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ESRK7F3LJNLBIB7MBIJ3J2JJKN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:ESRK7F3LJNLBIB7MBIJ3J2JJKN","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":"535c75e03fee86c7b23fff462c181e697adaa078bd1ab6df1a262a3e6db23080","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-10-12T09:59:19Z","title_canon_sha256":"c46cfc7e43490b4fd3fd702a3d4a93464fae070b40de68400187a00521ffa5fc"},"schema_version":"1.0","source":{"id":"1010.2342","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.2342","created_at":"2026-05-18T03:00:59Z"},{"alias_kind":"arxiv_version","alias_value":"1010.2342v3","created_at":"2026-05-18T03:00:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.2342","created_at":"2026-05-18T03:00:59Z"},{"alias_kind":"pith_short_12","alias_value":"ESRK7F3LJNLB","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"ESRK7F3LJNLBIB7M","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"ESRK7F3L","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:67f9cf02c52c5949b7daf1f2dae90664433b43378dbdb3f03611602d9b58a223","target":"graph","created_at":"2026-05-18T03:00:59Z","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":"Let $E$ be a finite dimensional vector space over a local field, and $F$ be its dual. For a closed subset $X$ of $E$, and $Y$ of $F$, consider the space $D^{-\\xi}(E;X,Y)$ of tempered distributions on $E$ whose support are contained in $X$ and support of whose Fourier transform are contained in $Y$. We show that $D^{-\\xi}(E;X,Y)$ possesses a certain rigidity property, for $X$, $Y$ which are some finite unions of affine subspaces.","authors_text":"Binyong Sun, Chen-bo Zhu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-10-12T09:59:19Z","title":"Fourier transform and rigidity of certain distributions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.2342","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":"sha256:324fe2ac899f402290d1773d33fee1c95fa6caa71717d0ed8e1f073c98b3c147","target":"record","created_at":"2026-05-18T03:00:59Z","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":"535c75e03fee86c7b23fff462c181e697adaa078bd1ab6df1a262a3e6db23080","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-10-12T09:59:19Z","title_canon_sha256":"c46cfc7e43490b4fd3fd702a3d4a93464fae070b40de68400187a00521ffa5fc"},"schema_version":"1.0","source":{"id":"1010.2342","kind":"arxiv","version":3}},"canonical_sha256":"24a2af976b4b561407ec0a13b4e92953599fc738229c3fc098279356cfcb07bf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"24a2af976b4b561407ec0a13b4e92953599fc738229c3fc098279356cfcb07bf","first_computed_at":"2026-05-18T03:00:59.672999Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:00:59.672999Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vU7Eh/EfY+FVdfVQimj7VsHYvOCffCRw4704FxN9xQvshHLNQ+GGV8X73xWl8CR9U10ct4OVJ+/riCw6Gc2sDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:00:59.673792Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.2342","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:324fe2ac899f402290d1773d33fee1c95fa6caa71717d0ed8e1f073c98b3c147","sha256:67f9cf02c52c5949b7daf1f2dae90664433b43378dbdb3f03611602d9b58a223"],"state_sha256":"6282127fd4000a70bcd1690cd2e3018b8118fe759844bf4f774fdff5487d56cd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nJfJJECNsTqivBsuqmPzRuwE5AFz2VSbO9gdGVdbWn9a3VIkyQqBW06RFgQeW91bkaTTMsNTplrYZoHuq6m/Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T20:49:02.373968Z","bundle_sha256":"5ab84a2dfb8e54f528823164c3fd219212dc29fdc826c54733045ef9a7de7561"}}