{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:6HJRRGPONK5KWCTPRHE4QSWZ3T","short_pith_number":"pith:6HJRRGPO","canonical_record":{"source":{"id":"1210.7711","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-10-29T16:19:38Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"8439b6668b89013f63898b41bf3424aea95407b17bc98ad0156d522e9d4d7e9a","abstract_canon_sha256":"5455d53f72ea68ea1bb8cc7255fd305d095a021569ea292b2918acdea572e20a"},"schema_version":"1.0"},"canonical_sha256":"f1d31899ee6abaab0a6f89c9c84ad9dce14c7bae1b08999098d3d0da9c499350","source":{"kind":"arxiv","id":"1210.7711","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.7711","created_at":"2026-05-18T03:42:09Z"},{"alias_kind":"arxiv_version","alias_value":"1210.7711v1","created_at":"2026-05-18T03:42:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.7711","created_at":"2026-05-18T03:42:09Z"},{"alias_kind":"pith_short_12","alias_value":"6HJRRGPONK5K","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6HJRRGPONK5KWCTP","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6HJRRGPO","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:6HJRRGPONK5KWCTPRHE4QSWZ3T","target":"record","payload":{"canonical_record":{"source":{"id":"1210.7711","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-10-29T16:19:38Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"8439b6668b89013f63898b41bf3424aea95407b17bc98ad0156d522e9d4d7e9a","abstract_canon_sha256":"5455d53f72ea68ea1bb8cc7255fd305d095a021569ea292b2918acdea572e20a"},"schema_version":"1.0"},"canonical_sha256":"f1d31899ee6abaab0a6f89c9c84ad9dce14c7bae1b08999098d3d0da9c499350","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:42:09.000805Z","signature_b64":"EcH2lav10vKLBwRRqLnB/sNkItgWE+HyqkyOr7JeQsCNZhjN9ytGwVMN5OThZrCIqy+7tx3NFJ2LngsGg52hDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f1d31899ee6abaab0a6f89c9c84ad9dce14c7bae1b08999098d3d0da9c499350","last_reissued_at":"2026-05-18T03:42:09Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:42:09Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.7711","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":"2026-05-18T03:42:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CYSZGyw42vhocnUnBewDTXZ7l7dxkYJ4iWP+y+3zZDrPsbFAHf2Awp44tgvqgRDCiQlJSSE+78tyWLuvRvyxCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T23:39:26.782639Z"},"content_sha256":"75d7eb5783927e7cc6158d939be0fbce9116cf8bec72655972f0c965e276c172","schema_version":"1.0","event_id":"sha256:75d7eb5783927e7cc6158d939be0fbce9116cf8bec72655972f0c965e276c172"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:6HJRRGPONK5KWCTPRHE4QSWZ3T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Refined support and entropic uncertainty inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Benjamin Ricaud, Bruno Torr\\'esani","submitted_at":"2012-10-29T16:19:38Z","abstract_excerpt":"Generalized versions of the entropic (Hirschman-Beckner) and support (Elad-Bruckstein) uncertainty principle are presented for frames representations. Moreover, a sharpened version of the support inequality has been obtained by introducing a generalization of the coherence. In the finite dimensional case and under certain conditions, minimizers of this inequalities are given as constant functions on their support. In addition, $\\ell^p$-norms inequalities are introduced as byproducts of the entropic inequalities."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.7711","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":"2026-05-18T03:42:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MIF0K/gA8MRrUK0pAHqPa924Uw5KKoPKWKDQ3yEGP5o/GT0QX7EW/ZPMbH3ct82dQEqyAZ53YBoWHJ1tw2LYDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T23:39:26.783102Z"},"content_sha256":"8cea1f580ee61feb01a270915899f5dfa43b6412ac9fa22f07678a6bc1427c2a","schema_version":"1.0","event_id":"sha256:8cea1f580ee61feb01a270915899f5dfa43b6412ac9fa22f07678a6bc1427c2a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6HJRRGPONK5KWCTPRHE4QSWZ3T/bundle.json","state_url":"https://pith.science/pith/6HJRRGPONK5KWCTPRHE4QSWZ3T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6HJRRGPONK5KWCTPRHE4QSWZ3T/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":"2026-06-25T23:39:26Z","links":{"resolver":"https://pith.science/pith/6HJRRGPONK5KWCTPRHE4QSWZ3T","bundle":"https://pith.science/pith/6HJRRGPONK5KWCTPRHE4QSWZ3T/bundle.json","state":"https://pith.science/pith/6HJRRGPONK5KWCTPRHE4QSWZ3T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6HJRRGPONK5KWCTPRHE4QSWZ3T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:6HJRRGPONK5KWCTPRHE4QSWZ3T","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":"5455d53f72ea68ea1bb8cc7255fd305d095a021569ea292b2918acdea572e20a","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-10-29T16:19:38Z","title_canon_sha256":"8439b6668b89013f63898b41bf3424aea95407b17bc98ad0156d522e9d4d7e9a"},"schema_version":"1.0","source":{"id":"1210.7711","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.7711","created_at":"2026-05-18T03:42:09Z"},{"alias_kind":"arxiv_version","alias_value":"1210.7711v1","created_at":"2026-05-18T03:42:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.7711","created_at":"2026-05-18T03:42:09Z"},{"alias_kind":"pith_short_12","alias_value":"6HJRRGPONK5K","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6HJRRGPONK5KWCTP","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6HJRRGPO","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:8cea1f580ee61feb01a270915899f5dfa43b6412ac9fa22f07678a6bc1427c2a","target":"graph","created_at":"2026-05-18T03:42:09Z","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":"Generalized versions of the entropic (Hirschman-Beckner) and support (Elad-Bruckstein) uncertainty principle are presented for frames representations. Moreover, a sharpened version of the support inequality has been obtained by introducing a generalization of the coherence. In the finite dimensional case and under certain conditions, minimizers of this inequalities are given as constant functions on their support. In addition, $\\ell^p$-norms inequalities are introduced as byproducts of the entropic inequalities.","authors_text":"Benjamin Ricaud, Bruno Torr\\'esani","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-10-29T16:19:38Z","title":"Refined support and entropic uncertainty inequalities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.7711","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":"sha256:75d7eb5783927e7cc6158d939be0fbce9116cf8bec72655972f0c965e276c172","target":"record","created_at":"2026-05-18T03:42:09Z","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":"5455d53f72ea68ea1bb8cc7255fd305d095a021569ea292b2918acdea572e20a","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-10-29T16:19:38Z","title_canon_sha256":"8439b6668b89013f63898b41bf3424aea95407b17bc98ad0156d522e9d4d7e9a"},"schema_version":"1.0","source":{"id":"1210.7711","kind":"arxiv","version":1}},"canonical_sha256":"f1d31899ee6abaab0a6f89c9c84ad9dce14c7bae1b08999098d3d0da9c499350","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f1d31899ee6abaab0a6f89c9c84ad9dce14c7bae1b08999098d3d0da9c499350","first_computed_at":"2026-05-18T03:42:09Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:42:09Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EcH2lav10vKLBwRRqLnB/sNkItgWE+HyqkyOr7JeQsCNZhjN9ytGwVMN5OThZrCIqy+7tx3NFJ2LngsGg52hDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:42:09.000805Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.7711","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:75d7eb5783927e7cc6158d939be0fbce9116cf8bec72655972f0c965e276c172","sha256:8cea1f580ee61feb01a270915899f5dfa43b6412ac9fa22f07678a6bc1427c2a"],"state_sha256":"2152522e1ac045dc4b4f4066a764b7406ff07d53328ed1cbcd204f2e8a986f70"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O+lx+SWlezuJxUywE35w6PPRWdtUt/uG1VWb6ZYyH6W939oFmDVp6VdzDBsNPQRax6+KkhIMd5H/yMoG2mbYDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T23:39:26.785427Z","bundle_sha256":"30245fe808e5f8d63aaf3ab7a1a53b9a59ae23144d8a5e03ff9e801c32f32178"}}