{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:4BRLYKPZGSYK7RC23FMTIHRDJG","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":"6b68c841ae6b6136ad916c64ddd7bcea218b28bc54ba78a47d518e0a229ba4f0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-06-01T23:29:02Z","title_canon_sha256":"b3c67de4ac1b27ce795c3980ef766f8e419760f8dfd0c2e023903262505923cb"},"schema_version":"1.0","source":{"id":"1106.0339","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.0339","created_at":"2026-05-18T01:22:54Z"},{"alias_kind":"arxiv_version","alias_value":"1106.0339v6","created_at":"2026-05-18T01:22:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.0339","created_at":"2026-05-18T01:22:54Z"},{"alias_kind":"pith_short_12","alias_value":"4BRLYKPZGSYK","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"4BRLYKPZGSYK7RC2","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"4BRLYKPZ","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:308d036f5ed789290f540ff6f959602296f0d1f649005cec8c1f8b9830327434","target":"graph","created_at":"2026-05-18T01:22:54Z","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 bounded linear operator $T$ on a Banach space $X$ is called an $(m, p)$-isometry if it satisfies the equation \\sum_{k=0}^{m}(-1)^{k} {m \\choose k}\\|T^{k}x\\|^{p} = 0$, for all $x \\in X$. In this paper we study the structure which underlies the second parameter of $(m, p)$-isometric operators. We concentrate on determining when an $(m, p)$-isometry is a $(\\mu, q)$-isometry for some pair ($\\mu, q)$. We also extend the definition of $(m, p)$-isometry, to include $p=\\infty$ and study basic properties of these $(m, \\infty)$-isometries.","authors_text":"Michael Mackey, M\\'iche\\'al \\'O Searc\\'oid, Philipp Hoffmann","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-06-01T23:29:02Z","title":"On the second parameter of an $(m, p)$-isometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.0339","kind":"arxiv","version":6},"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":"sha256:0e167a82c6572ae8515e4bb9b46b447331e9de41bf6c6b3f7927297fc5bf7c4d","target":"record","created_at":"2026-05-18T01:22:54Z","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":"6b68c841ae6b6136ad916c64ddd7bcea218b28bc54ba78a47d518e0a229ba4f0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-06-01T23:29:02Z","title_canon_sha256":"b3c67de4ac1b27ce795c3980ef766f8e419760f8dfd0c2e023903262505923cb"},"schema_version":"1.0","source":{"id":"1106.0339","kind":"arxiv","version":6}},"canonical_sha256":"e062bc29f934b0afc45ad959341e2349978538c4d95991a579d766b70ccbe990","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e062bc29f934b0afc45ad959341e2349978538c4d95991a579d766b70ccbe990","first_computed_at":"2026-05-18T01:22:54.536460Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:54.536460Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j8LT+kGpMod6IEw7q0mznDbat1yvE8dflkpmuJR1h9+BI44cmCi77+BPRhvoO0w07b39nbm+bMdW0vmOyZP2Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:54.537074Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.0339","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0e167a82c6572ae8515e4bb9b46b447331e9de41bf6c6b3f7927297fc5bf7c4d","sha256:308d036f5ed789290f540ff6f959602296f0d1f649005cec8c1f8b9830327434"],"state_sha256":"b83343b995949319ea1709e60e9ace38111b0f45b5657f662d2b59a1206b2c77"}