{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2002:XIWLSEXOFSCSIYC525BGSCSBUX","short_pith_number":"pith:XIWLSEXO","schema_version":"1.0","canonical_sha256":"ba2cb912ee2c8524605dd742690a41a5ef8772758b06676eeeec57f3b7dd434a","source":{"kind":"arxiv","id":"gr-qc/0207112","version":3},"attestation_state":"computed","paper":{"title":"When Do Measures on the Space of Connections Support the Triad Operators of Loop Quantum Gravity?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"gr-qc","authors_text":"Hanno Sahlmann","submitted_at":"2002-07-29T15:54:12Z","abstract_excerpt":"In this work we investigate the question, under what conditions Hilbert spaces that are induced by measures on the space of generalized connections carry a representation of certain non-Abelian analogues of the electric flux. We give the problem a precise mathematical formulation and start its investigation. For the technically simple case of U(1) as gauge group, we establish a number of \"no-go theorems\" asserting that for certain classes of measures, the flux operators can not be represented on the corresponding Hilbert spaces.\n  The flux-observables we consider play an important role in loop"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"gr-qc/0207112","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2002-07-29T15:54:12Z","cross_cats_sorted":["hep-th","math-ph","math.MP"],"title_canon_sha256":"c8a83f70d229b174a0730ff4227315ef6f3fefd9e10d80b6118a46d03ccab73a","abstract_canon_sha256":"dce753c69cda851a513abb9ed87b93da99a55cffe7fb69e093c80e3050eeda33"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:30:46.681327Z","signature_b64":"SBsDIREijFHsUuRHcZl8WhNr9pnpu5KVZdYmLuXTcA/POUOGISHcaUB1k8GwdyOK9wn4fU8MCf19GXx3aQfCDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ba2cb912ee2c8524605dd742690a41a5ef8772758b06676eeeec57f3b7dd434a","last_reissued_at":"2026-05-18T04:30:46.680429Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:30:46.680429Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"When Do Measures on the Space of Connections Support the Triad Operators of Loop Quantum Gravity?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"gr-qc","authors_text":"Hanno Sahlmann","submitted_at":"2002-07-29T15:54:12Z","abstract_excerpt":"In this work we investigate the question, under what conditions Hilbert spaces that are induced by measures on the space of generalized connections carry a representation of certain non-Abelian analogues of the electric flux. We give the problem a precise mathematical formulation and start its investigation. For the technically simple case of U(1) as gauge group, we establish a number of \"no-go theorems\" asserting that for certain classes of measures, the flux operators can not be represented on the corresponding Hilbert spaces.\n  The flux-observables we consider play an important role in loop"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/0207112","kind":"arxiv","version":3},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/0207112","created_at":"2026-05-18T04:30:46.680517+00:00"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/0207112v3","created_at":"2026-05-18T04:30:46.680517+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/0207112","created_at":"2026-05-18T04:30:46.680517+00:00"},{"alias_kind":"pith_short_12","alias_value":"XIWLSEXOFSCS","created_at":"2026-05-18T12:25:51.375804+00:00"},{"alias_kind":"pith_short_16","alias_value":"XIWLSEXOFSCSIYC5","created_at":"2026-05-18T12:25:51.375804+00:00"},{"alias_kind":"pith_short_8","alias_value":"XIWLSEXO","created_at":"2026-05-18T12:25:51.375804+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XIWLSEXOFSCSIYC525BGSCSBUX","json":"https://pith.science/pith/XIWLSEXOFSCSIYC525BGSCSBUX.json","graph_json":"https://pith.science/api/pith-number/XIWLSEXOFSCSIYC525BGSCSBUX/graph.json","events_json":"https://pith.science/api/pith-number/XIWLSEXOFSCSIYC525BGSCSBUX/events.json","paper":"https://pith.science/paper/XIWLSEXO"},"agent_actions":{"view_html":"https://pith.science/pith/XIWLSEXOFSCSIYC525BGSCSBUX","download_json":"https://pith.science/pith/XIWLSEXOFSCSIYC525BGSCSBUX.json","view_paper":"https://pith.science/paper/XIWLSEXO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=gr-qc/0207112&json=true","fetch_graph":"https://pith.science/api/pith-number/XIWLSEXOFSCSIYC525BGSCSBUX/graph.json","fetch_events":"https://pith.science/api/pith-number/XIWLSEXOFSCSIYC525BGSCSBUX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XIWLSEXOFSCSIYC525BGSCSBUX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XIWLSEXOFSCSIYC525BGSCSBUX/action/storage_attestation","attest_author":"https://pith.science/pith/XIWLSEXOFSCSIYC525BGSCSBUX/action/author_attestation","sign_citation":"https://pith.science/pith/XIWLSEXOFSCSIYC525BGSCSBUX/action/citation_signature","submit_replication":"https://pith.science/pith/XIWLSEXOFSCSIYC525BGSCSBUX/action/replication_record"}},"created_at":"2026-05-18T04:30:46.680517+00:00","updated_at":"2026-05-18T04:30:46.680517+00:00"}