{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:UQP2SKQABYSRHCG2C734UARSFJ","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":"b4f8b8e114d51e0cdc39322c65c98185d60807f8307a65a003ea6bad1943dce6","cross_cats_sorted":["cs.IT","math.GN","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-02-09T20:01:22Z","title_canon_sha256":"b3948a9388ae3d9dfd2a7fd363e5f88771c4bbff75321e93c9bb92a83d7fd7af"},"schema_version":"1.0","source":{"id":"1502.02635","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.02635","created_at":"2026-05-18T02:27:41Z"},{"alias_kind":"arxiv_version","alias_value":"1502.02635v1","created_at":"2026-05-18T02:27:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.02635","created_at":"2026-05-18T02:27:41Z"},{"alias_kind":"pith_short_12","alias_value":"UQP2SKQABYSR","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UQP2SKQABYSRHCG2","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UQP2SKQA","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:1eb808c17a9b07819408548766e5dd450945d34bee07bdbe6d845a3f41038782","target":"graph","created_at":"2026-05-18T02:27:41Z","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 $\\mathbb F$ be a finite field and let $\\mathcal A$ and $\\mathcal B$ be vector spaces of $\\mathbb F$-valued continuous functions defined on locally compact spaces $X$ and $Y$, respectively. We look at the representation of linear bijections $H:\\mathcal A\\longrightarrow \\mathcal B$ by continuous functions $h:Y\\longrightarrow X$ as weighted composition operators. In order to do it, we extend the notion of Hamming metric to infinite spaces. Our main result establishes that under some mild conditions, every Hamming isometry can be represented as a weighted composition operator. Connections to c","authors_text":"Margarita Gary, Marita Ferrer, Salvador Hernandez","cross_cats":["cs.IT","math.GN","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-02-09T20:01:22Z","title":"Weight-preserving isomorphisms between spaces of continuous functions: The scalar case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.02635","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":"sha256:75e3dcd2fafdb73dea42ca6f4c883a530c8b4e16f4c08089ed22ec68603a0c8d","target":"record","created_at":"2026-05-18T02:27:41Z","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":"b4f8b8e114d51e0cdc39322c65c98185d60807f8307a65a003ea6bad1943dce6","cross_cats_sorted":["cs.IT","math.GN","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-02-09T20:01:22Z","title_canon_sha256":"b3948a9388ae3d9dfd2a7fd363e5f88771c4bbff75321e93c9bb92a83d7fd7af"},"schema_version":"1.0","source":{"id":"1502.02635","kind":"arxiv","version":1}},"canonical_sha256":"a41fa92a000e251388da17f7ca02322a6d84eef2658cdb47ace90da41de531bf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a41fa92a000e251388da17f7ca02322a6d84eef2658cdb47ace90da41de531bf","first_computed_at":"2026-05-18T02:27:41.596791Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:41.596791Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1k7NYfjWT0UaYel1LtkvDkTMNHbYcus10tnSqIDP6znsRDRVO2iJXzIcCzNhB9GTKdM3XIixKa/GJqW9ucULCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:41.597746Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.02635","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:75e3dcd2fafdb73dea42ca6f4c883a530c8b4e16f4c08089ed22ec68603a0c8d","sha256:1eb808c17a9b07819408548766e5dd450945d34bee07bdbe6d845a3f41038782"],"state_sha256":"fc642c5063f4e6e97fd59b9a3d3b45b56ab334dec696676c8ff4ebbf6735309b"}