{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2004:4HAH7IABSIDY7L3OJHPTCETDU3","short_pith_number":"pith:4HAH7IAB","schema_version":"1.0","canonical_sha256":"e1c07fa00192078faf6e49df311263a6e8a0dd9547993ba1f2966686aaf552ec","source":{"kind":"arxiv","id":"gr-qc/0403047","version":2},"attestation_state":"computed","paper":{"title":"Separable Hilbert space in Loop Quantum Gravity","license":"","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Carlo Rovelli, Winston Fairbairn","submitted_at":"2004-03-11T17:46:55Z","abstract_excerpt":"We study the separability of the state space of loop quantum gravity. In the standard construction, the kinematical Hilbert space of the diffeomorphism-invariant states is nonseparable. This is a consequence of the fact that the knot-space of the equivalence classes of graphs under diffeomorphisms is noncountable. However, the continuous moduli labeling these classes do not appear to affect the physics of the theory. We investigate the possibility that these moduli could be only the consequence of a poor choice in the fine-tuning of the mathematical setting. We show that by simply choosing a m"},"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/0403047","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"2004-03-11T17:46:55Z","cross_cats_sorted":[],"title_canon_sha256":"d72ed2e570dfb4dd1ec1b041b798a7e3b9e4290cbec86e109515f5011529d3ed","abstract_canon_sha256":"cdbaa59f255f2dbde85e5210478d1e3381414f8be5b8d2e1f98f2e8ca2cd09bb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:39:22.622835Z","signature_b64":"rDPKAda3fG7usROV2XLNnF2E6E0F0+anxkOTs/bh8u2UZ+1ZMDrx6hfU0jceX/UtiAiFoe3YwrqX1QH80WajAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e1c07fa00192078faf6e49df311263a6e8a0dd9547993ba1f2966686aaf552ec","last_reissued_at":"2026-05-18T01:39:22.622231Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:39:22.622231Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Separable Hilbert space in Loop Quantum Gravity","license":"","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Carlo Rovelli, Winston Fairbairn","submitted_at":"2004-03-11T17:46:55Z","abstract_excerpt":"We study the separability of the state space of loop quantum gravity. In the standard construction, the kinematical Hilbert space of the diffeomorphism-invariant states is nonseparable. This is a consequence of the fact that the knot-space of the equivalence classes of graphs under diffeomorphisms is noncountable. However, the continuous moduli labeling these classes do not appear to affect the physics of the theory. We investigate the possibility that these moduli could be only the consequence of a poor choice in the fine-tuning of the mathematical setting. We show that by simply choosing a m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/0403047","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":""},"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/0403047","created_at":"2026-05-18T01:39:22.622325+00:00"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/0403047v2","created_at":"2026-05-18T01:39:22.622325+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/0403047","created_at":"2026-05-18T01:39:22.622325+00:00"},{"alias_kind":"pith_short_12","alias_value":"4HAH7IABSIDY","created_at":"2026-05-18T12:25:52.051335+00:00"},{"alias_kind":"pith_short_16","alias_value":"4HAH7IABSIDY7L3O","created_at":"2026-05-18T12:25:52.051335+00:00"},{"alias_kind":"pith_short_8","alias_value":"4HAH7IAB","created_at":"2026-05-18T12:25:52.051335+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2502.08494","citing_title":"All Hilbert spaces are the same: consequences for generalized coordinates and momenta","ref_index":44,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4HAH7IABSIDY7L3OJHPTCETDU3","json":"https://pith.science/pith/4HAH7IABSIDY7L3OJHPTCETDU3.json","graph_json":"https://pith.science/api/pith-number/4HAH7IABSIDY7L3OJHPTCETDU3/graph.json","events_json":"https://pith.science/api/pith-number/4HAH7IABSIDY7L3OJHPTCETDU3/events.json","paper":"https://pith.science/paper/4HAH7IAB"},"agent_actions":{"view_html":"https://pith.science/pith/4HAH7IABSIDY7L3OJHPTCETDU3","download_json":"https://pith.science/pith/4HAH7IABSIDY7L3OJHPTCETDU3.json","view_paper":"https://pith.science/paper/4HAH7IAB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=gr-qc/0403047&json=true","fetch_graph":"https://pith.science/api/pith-number/4HAH7IABSIDY7L3OJHPTCETDU3/graph.json","fetch_events":"https://pith.science/api/pith-number/4HAH7IABSIDY7L3OJHPTCETDU3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4HAH7IABSIDY7L3OJHPTCETDU3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4HAH7IABSIDY7L3OJHPTCETDU3/action/storage_attestation","attest_author":"https://pith.science/pith/4HAH7IABSIDY7L3OJHPTCETDU3/action/author_attestation","sign_citation":"https://pith.science/pith/4HAH7IABSIDY7L3OJHPTCETDU3/action/citation_signature","submit_replication":"https://pith.science/pith/4HAH7IABSIDY7L3OJHPTCETDU3/action/replication_record"}},"created_at":"2026-05-18T01:39:22.622325+00:00","updated_at":"2026-05-18T01:39:22.622325+00:00"}