{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:JW4BSDKSHBANMGXN7N2E3VRTTI","short_pith_number":"pith:JW4BSDKS","canonical_record":{"source":{"id":"2503.04938","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2025-03-06T20:13:29Z","cross_cats_sorted":["math.MP","math.OA"],"title_canon_sha256":"3de1eb0af7bc0c69c24e2f58fbee6baf2dad312804699e433b3912f22f083142","abstract_canon_sha256":"2a50e157e35897593dd50e686050b3c6a2c12bdf01cf3a6ac2300a9a38c4704e"},"schema_version":"1.0"},"canonical_sha256":"4db8190d523840d61aedfb744dd6339a305bb21a761b5370f1c2b8ebd250acb6","source":{"kind":"arxiv","id":"2503.04938","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.04938","created_at":"2026-07-05T10:38:43Z"},{"alias_kind":"arxiv_version","alias_value":"2503.04938v2","created_at":"2026-07-05T10:38:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.04938","created_at":"2026-07-05T10:38:43Z"},{"alias_kind":"pith_short_12","alias_value":"JW4BSDKSHBAN","created_at":"2026-07-05T10:38:43Z"},{"alias_kind":"pith_short_16","alias_value":"JW4BSDKSHBANMGXN","created_at":"2026-07-05T10:38:43Z"},{"alias_kind":"pith_short_8","alias_value":"JW4BSDKS","created_at":"2026-07-05T10:38:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:JW4BSDKSHBANMGXN7N2E3VRTTI","target":"record","payload":{"canonical_record":{"source":{"id":"2503.04938","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2025-03-06T20:13:29Z","cross_cats_sorted":["math.MP","math.OA"],"title_canon_sha256":"3de1eb0af7bc0c69c24e2f58fbee6baf2dad312804699e433b3912f22f083142","abstract_canon_sha256":"2a50e157e35897593dd50e686050b3c6a2c12bdf01cf3a6ac2300a9a38c4704e"},"schema_version":"1.0"},"canonical_sha256":"4db8190d523840d61aedfb744dd6339a305bb21a761b5370f1c2b8ebd250acb6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:38:43.808702Z","signature_b64":"95gnn93SHQ1Mgc3doSnchwBgpixG5Vop4iY7C4aSDWN/AgCqlIsXLLb33gvocPvTZnPr99j3P/gLp/BdEbIEDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4db8190d523840d61aedfb744dd6339a305bb21a761b5370f1c2b8ebd250acb6","last_reissued_at":"2026-07-05T10:38:43.808216Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:38:43.808216Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2503.04938","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:38:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M8OwigGzjjOu4mw2czEJgXWXwrS8d5BAlijda2viKAvSdFIMPX2u6YNAe+2m3k9lSzgvwUqc+bjtgPAWsiBBAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T07:39:38.202971Z"},"content_sha256":"cdb1f008ada5cdfa3e7c27f5f447d32225122cdf19529cdf7345444a44389f20","schema_version":"1.0","event_id":"sha256:cdb1f008ada5cdfa3e7c27f5f447d32225122cdf19529cdf7345444a44389f20"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:JW4BSDKSHBANMGXN7N2E3VRTTI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Topological description of pure invariant states of the Weyl $C^*$-algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.OA"],"primary_cat":"math-ph","authors_text":"Giuseppe De Nittis, Santiago G. Rendel","submitted_at":"2025-03-06T20:13:29Z","abstract_excerpt":"In this work we study the topology of certain families of states of the Weyl $C^*$-algebra with finite degrees of freedom. We focus on families of pure states characterized by symmetries and a (semi-)regularity condition, and obtain precise topological descriptions through homeomorphisms with other explicit spaces. Of special importance are the families of pure, semi-regular states invariant under either continuous (plane-wave states) or discrete (Bloch-wave states) spatial translations, and the family of states invariant under discrete, mutually commuting spatial and momentum translations (Za"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.04938","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2503.04938/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T10:38:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l+l3q5ZjVZbFn0yw08o/d9NbZH0L2t4dawlaoNy8MtDWEZpYfElOT9T5tAA0YqPGqqToJz4qmI++rMh7WClkCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T07:39:38.203479Z"},"content_sha256":"89ac9700dacc603f956c23c9e4dfe13ae55c2d2358581d91b96630190f0b9ed2","schema_version":"1.0","event_id":"sha256:89ac9700dacc603f956c23c9e4dfe13ae55c2d2358581d91b96630190f0b9ed2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JW4BSDKSHBANMGXN7N2E3VRTTI/bundle.json","state_url":"https://pith.science/pith/JW4BSDKSHBANMGXN7N2E3VRTTI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JW4BSDKSHBANMGXN7N2E3VRTTI/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":"2026-07-06T07:39:38Z","links":{"resolver":"https://pith.science/pith/JW4BSDKSHBANMGXN7N2E3VRTTI","bundle":"https://pith.science/pith/JW4BSDKSHBANMGXN7N2E3VRTTI/bundle.json","state":"https://pith.science/pith/JW4BSDKSHBANMGXN7N2E3VRTTI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JW4BSDKSHBANMGXN7N2E3VRTTI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:JW4BSDKSHBANMGXN7N2E3VRTTI","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":"2a50e157e35897593dd50e686050b3c6a2c12bdf01cf3a6ac2300a9a38c4704e","cross_cats_sorted":["math.MP","math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2025-03-06T20:13:29Z","title_canon_sha256":"3de1eb0af7bc0c69c24e2f58fbee6baf2dad312804699e433b3912f22f083142"},"schema_version":"1.0","source":{"id":"2503.04938","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.04938","created_at":"2026-07-05T10:38:43Z"},{"alias_kind":"arxiv_version","alias_value":"2503.04938v2","created_at":"2026-07-05T10:38:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.04938","created_at":"2026-07-05T10:38:43Z"},{"alias_kind":"pith_short_12","alias_value":"JW4BSDKSHBAN","created_at":"2026-07-05T10:38:43Z"},{"alias_kind":"pith_short_16","alias_value":"JW4BSDKSHBANMGXN","created_at":"2026-07-05T10:38:43Z"},{"alias_kind":"pith_short_8","alias_value":"JW4BSDKS","created_at":"2026-07-05T10:38:43Z"}],"graph_snapshots":[{"event_id":"sha256:89ac9700dacc603f956c23c9e4dfe13ae55c2d2358581d91b96630190f0b9ed2","target":"graph","created_at":"2026-07-05T10:38:43Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2503.04938/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this work we study the topology of certain families of states of the Weyl $C^*$-algebra with finite degrees of freedom. We focus on families of pure states characterized by symmetries and a (semi-)regularity condition, and obtain precise topological descriptions through homeomorphisms with other explicit spaces. Of special importance are the families of pure, semi-regular states invariant under either continuous (plane-wave states) or discrete (Bloch-wave states) spatial translations, and the family of states invariant under discrete, mutually commuting spatial and momentum translations (Za","authors_text":"Giuseppe De Nittis, Santiago G. Rendel","cross_cats":["math.MP","math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2025-03-06T20:13:29Z","title":"Topological description of pure invariant states of the Weyl $C^*$-algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.04938","kind":"arxiv","version":2},"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:cdb1f008ada5cdfa3e7c27f5f447d32225122cdf19529cdf7345444a44389f20","target":"record","created_at":"2026-07-05T10:38:43Z","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":"2a50e157e35897593dd50e686050b3c6a2c12bdf01cf3a6ac2300a9a38c4704e","cross_cats_sorted":["math.MP","math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2025-03-06T20:13:29Z","title_canon_sha256":"3de1eb0af7bc0c69c24e2f58fbee6baf2dad312804699e433b3912f22f083142"},"schema_version":"1.0","source":{"id":"2503.04938","kind":"arxiv","version":2}},"canonical_sha256":"4db8190d523840d61aedfb744dd6339a305bb21a761b5370f1c2b8ebd250acb6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4db8190d523840d61aedfb744dd6339a305bb21a761b5370f1c2b8ebd250acb6","first_computed_at":"2026-07-05T10:38:43.808216Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:38:43.808216Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"95gnn93SHQ1Mgc3doSnchwBgpixG5Vop4iY7C4aSDWN/AgCqlIsXLLb33gvocPvTZnPr99j3P/gLp/BdEbIEDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:38:43.808702Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.04938","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cdb1f008ada5cdfa3e7c27f5f447d32225122cdf19529cdf7345444a44389f20","sha256:89ac9700dacc603f956c23c9e4dfe13ae55c2d2358581d91b96630190f0b9ed2"],"state_sha256":"ed3c52209e5572971cb422ac68df52620a86acb79de5ab0a36db31c27252aab9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5xQSh3DU/a9RD5tDL4gkr798A4ZYaI0522HlLDEi5s8vHRBMBVV5iGyxflFEVJI9Uz/ANpYbEQnt3py8AdJGBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T07:39:38.205477Z","bundle_sha256":"888515fe9f961b28081d2a8e4f10700005fe8350cb0037edf14058f17d281937"}}