{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:GBNB7N6ELKAFHT4I5KGFERT4XV","short_pith_number":"pith:GBNB7N6E","canonical_record":{"source":{"id":"1606.01704","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-06-06T11:51:21Z","cross_cats_sorted":[],"title_canon_sha256":"da2712064aa5999bb14e4ccedd51e80149f7ce979b52614473718c95c1f61e74","abstract_canon_sha256":"a9592451620eea2d5280234c07737aab56633c0dea3a9b53776c28afe6afccf1"},"schema_version":"1.0"},"canonical_sha256":"305a1fb7c45a8053cf88ea8c52467cbd6db708b123d1f010a98550f37c5ecc29","source":{"kind":"arxiv","id":"1606.01704","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.01704","created_at":"2026-05-18T01:12:53Z"},{"alias_kind":"arxiv_version","alias_value":"1606.01704v1","created_at":"2026-05-18T01:12:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.01704","created_at":"2026-05-18T01:12:53Z"},{"alias_kind":"pith_short_12","alias_value":"GBNB7N6ELKAF","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"GBNB7N6ELKAFHT4I","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"GBNB7N6E","created_at":"2026-05-18T12:30:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:GBNB7N6ELKAFHT4I5KGFERT4XV","target":"record","payload":{"canonical_record":{"source":{"id":"1606.01704","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-06-06T11:51:21Z","cross_cats_sorted":[],"title_canon_sha256":"da2712064aa5999bb14e4ccedd51e80149f7ce979b52614473718c95c1f61e74","abstract_canon_sha256":"a9592451620eea2d5280234c07737aab56633c0dea3a9b53776c28afe6afccf1"},"schema_version":"1.0"},"canonical_sha256":"305a1fb7c45a8053cf88ea8c52467cbd6db708b123d1f010a98550f37c5ecc29","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:53.763787Z","signature_b64":"BSOpsTrcfRnBjzoFdwLkoqf+UTYpqEal5l/N2MOu+yaWR7ltfVzAmzkkabr9X39qEHh4GbVQbLw8ZPOTC+u3CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"305a1fb7c45a8053cf88ea8c52467cbd6db708b123d1f010a98550f37c5ecc29","last_reissued_at":"2026-05-18T01:12:53.763458Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:53.763458Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.01704","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":"2026-05-18T01:12:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5HZf6UECnSOI2MYa+Sr/mAfRWDgLFsBmrCf7COphRtWKKyBt8DFI5ge+Wg51kDmifprnVAgrm8VsQUiu+H1qDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T16:33:49.985553Z"},"content_sha256":"02c09585ddaf42a87d32d93a0d11b6eef8fa3bc9c01159520917417e646b8150","schema_version":"1.0","event_id":"sha256:02c09585ddaf42a87d32d93a0d11b6eef8fa3bc9c01159520917417e646b8150"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:GBNB7N6ELKAFHT4I5KGFERT4XV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An Uncertainty Principle of Paley and Wiener on Euclidean Motion Group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Mithun Bhowmik, Suparna Sen","submitted_at":"2016-06-06T11:51:21Z","abstract_excerpt":"A classical result due to Paley and Wiener characterizes the existence of a non-zero function in $L^2(\\mathbb{R})$, supported on a half line, in terms of the decay of its Fourier transform. In this paper we prove an analogue of this result for compactly supported continuous functions on the Euclidean motion group $M(n)$. We also relate this result to a uniqueness property of solutions to the initial value problem for time-dependent Schr\\\"odinger equation on $M(n)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.01704","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":""},"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":"2026-05-18T01:12:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/FAPYmq+gGORICQVVEHVW4KUAzOOqEYCgJulDReZ0Ikqr8QjfKPmXRauyw0Ox4vPGIUD5kyEArwhPDEcUKtSAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T16:33:49.986037Z"},"content_sha256":"6ed24e0a825d64b8f25b1d278d3f7acc8beae3cb052203b849e83b18b39033fc","schema_version":"1.0","event_id":"sha256:6ed24e0a825d64b8f25b1d278d3f7acc8beae3cb052203b849e83b18b39033fc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GBNB7N6ELKAFHT4I5KGFERT4XV/bundle.json","state_url":"https://pith.science/pith/GBNB7N6ELKAFHT4I5KGFERT4XV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GBNB7N6ELKAFHT4I5KGFERT4XV/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":"2026-06-22T16:33:49Z","links":{"resolver":"https://pith.science/pith/GBNB7N6ELKAFHT4I5KGFERT4XV","bundle":"https://pith.science/pith/GBNB7N6ELKAFHT4I5KGFERT4XV/bundle.json","state":"https://pith.science/pith/GBNB7N6ELKAFHT4I5KGFERT4XV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GBNB7N6ELKAFHT4I5KGFERT4XV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:GBNB7N6ELKAFHT4I5KGFERT4XV","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":"a9592451620eea2d5280234c07737aab56633c0dea3a9b53776c28afe6afccf1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-06-06T11:51:21Z","title_canon_sha256":"da2712064aa5999bb14e4ccedd51e80149f7ce979b52614473718c95c1f61e74"},"schema_version":"1.0","source":{"id":"1606.01704","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.01704","created_at":"2026-05-18T01:12:53Z"},{"alias_kind":"arxiv_version","alias_value":"1606.01704v1","created_at":"2026-05-18T01:12:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.01704","created_at":"2026-05-18T01:12:53Z"},{"alias_kind":"pith_short_12","alias_value":"GBNB7N6ELKAF","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"GBNB7N6ELKAFHT4I","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"GBNB7N6E","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:6ed24e0a825d64b8f25b1d278d3f7acc8beae3cb052203b849e83b18b39033fc","target":"graph","created_at":"2026-05-18T01:12:53Z","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":"A classical result due to Paley and Wiener characterizes the existence of a non-zero function in $L^2(\\mathbb{R})$, supported on a half line, in terms of the decay of its Fourier transform. In this paper we prove an analogue of this result for compactly supported continuous functions on the Euclidean motion group $M(n)$. We also relate this result to a uniqueness property of solutions to the initial value problem for time-dependent Schr\\\"odinger equation on $M(n)$.","authors_text":"Mithun Bhowmik, Suparna Sen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-06-06T11:51:21Z","title":"An Uncertainty Principle of Paley and Wiener on Euclidean Motion Group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.01704","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":"sha256:02c09585ddaf42a87d32d93a0d11b6eef8fa3bc9c01159520917417e646b8150","target":"record","created_at":"2026-05-18T01:12:53Z","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":"a9592451620eea2d5280234c07737aab56633c0dea3a9b53776c28afe6afccf1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-06-06T11:51:21Z","title_canon_sha256":"da2712064aa5999bb14e4ccedd51e80149f7ce979b52614473718c95c1f61e74"},"schema_version":"1.0","source":{"id":"1606.01704","kind":"arxiv","version":1}},"canonical_sha256":"305a1fb7c45a8053cf88ea8c52467cbd6db708b123d1f010a98550f37c5ecc29","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"305a1fb7c45a8053cf88ea8c52467cbd6db708b123d1f010a98550f37c5ecc29","first_computed_at":"2026-05-18T01:12:53.763458Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:53.763458Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BSOpsTrcfRnBjzoFdwLkoqf+UTYpqEal5l/N2MOu+yaWR7ltfVzAmzkkabr9X39qEHh4GbVQbLw8ZPOTC+u3CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:53.763787Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.01704","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:02c09585ddaf42a87d32d93a0d11b6eef8fa3bc9c01159520917417e646b8150","sha256:6ed24e0a825d64b8f25b1d278d3f7acc8beae3cb052203b849e83b18b39033fc"],"state_sha256":"a4f101e6446c832be0aba144680a858b291567e03844d34c41e74e5733372461"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SphIYZnPscyvoz3nMjrCTeipkAsfdiI5AORXz9DXHiJToQjXSVflKHBjwBFdF1CAC1T1eZkQ7eRkhQhmJUD0BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T16:33:49.988635Z","bundle_sha256":"781e25d6bdce63288d5a8cf64688d6557145e4db537b27673ef46009aecb39f8"}}