{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:P3XEWQ2NC6C5OCRUPMJZ7SCFOK","short_pith_number":"pith:P3XEWQ2N","canonical_record":{"source":{"id":"2003.03952","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2020-03-09T07:25:54Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"af77b928fd204e3b7ed9ab8f7f39c0780fee020980e008b3bce319e3e77eecd2","abstract_canon_sha256":"fd2116d431f835ceda6de7eddeccc29b3f1b047bb65224b68f822fb2d4bb1c44"},"schema_version":"1.0"},"canonical_sha256":"7eee4b434d1785d70a347b139fc84572841b014b87fd7cb10d89bbe60848f8a9","source":{"kind":"arxiv","id":"2003.03952","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2003.03952","created_at":"2026-07-05T00:57:18Z"},{"alias_kind":"arxiv_version","alias_value":"2003.03952v1","created_at":"2026-07-05T00:57:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2003.03952","created_at":"2026-07-05T00:57:18Z"},{"alias_kind":"pith_short_12","alias_value":"P3XEWQ2NC6C5","created_at":"2026-07-05T00:57:18Z"},{"alias_kind":"pith_short_16","alias_value":"P3XEWQ2NC6C5OCRU","created_at":"2026-07-05T00:57:18Z"},{"alias_kind":"pith_short_8","alias_value":"P3XEWQ2N","created_at":"2026-07-05T00:57:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:P3XEWQ2NC6C5OCRUPMJZ7SCFOK","target":"record","payload":{"canonical_record":{"source":{"id":"2003.03952","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2020-03-09T07:25:54Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"af77b928fd204e3b7ed9ab8f7f39c0780fee020980e008b3bce319e3e77eecd2","abstract_canon_sha256":"fd2116d431f835ceda6de7eddeccc29b3f1b047bb65224b68f822fb2d4bb1c44"},"schema_version":"1.0"},"canonical_sha256":"7eee4b434d1785d70a347b139fc84572841b014b87fd7cb10d89bbe60848f8a9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:57:18.951710Z","signature_b64":"kGjW2N1xtM4pXSvzqMsj/ZtDJkodOJaNbbG1ifGfXI+5HFSsJM6ENWDtFc/HAgSE12yKP/Mqa2Mj3AwHstJTDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7eee4b434d1785d70a347b139fc84572841b014b87fd7cb10d89bbe60848f8a9","last_reissued_at":"2026-07-05T00:57:18.951274Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:57:18.951274Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2003.03952","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:57:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QFFWQ91lCCSUVkG1uhqidByqkJvfjvVW6pRspqyQRpqqndA+ouUWCHw5t29bE2s6M3wHOdsqTtv8nqyOZ1WvAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T12:39:26.968395Z"},"content_sha256":"77d410c938a0b33bbf21402db277de1d88719ad14f04ee6d036635ec43244f83","schema_version":"1.0","event_id":"sha256:77d410c938a0b33bbf21402db277de1d88719ad14f04ee6d036635ec43244f83"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:P3XEWQ2NC6C5OCRUPMJZ7SCFOK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"General geometric operators in all dimensional loop quantum gravity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"gr-qc","authors_text":"Gaoping Long, Yongge Ma","submitted_at":"2020-03-09T07:25:54Z","abstract_excerpt":"Two strategies for constructing general geometric operators in all dimensional loop quantum gravity are proposed. The different constructions are mainly come from the two different regularization methods for the de-densitized dual momentum, which play the role of building block for the spatial geometry. The first regularization method is a generalization of the regularization of the length operator in standard $(1+3)$-dimensional loop quantum gravity, while the second method is a natural extension of those for standard (D-1)-area and D-volume operators. Two versions of general geometric operat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2003.03952","kind":"arxiv","version":1},"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/2003.03952/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":"2026-07-05T00:57:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dzsnFwqTmd5tjqlojLlQpcOJeQakufp6/U8VbA+5hbPLW2VnrqVu0gdyqgLDbX1VBQID+BO+EuKUixBnMND5DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T12:39:26.969345Z"},"content_sha256":"1f7055acae7944b86856bf94b5bf64efbabdb1a456f3f7f0a0a38cc7cb4383fc","schema_version":"1.0","event_id":"sha256:1f7055acae7944b86856bf94b5bf64efbabdb1a456f3f7f0a0a38cc7cb4383fc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P3XEWQ2NC6C5OCRUPMJZ7SCFOK/bundle.json","state_url":"https://pith.science/pith/P3XEWQ2NC6C5OCRUPMJZ7SCFOK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P3XEWQ2NC6C5OCRUPMJZ7SCFOK/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":"2026-08-11T12:39:26Z","links":{"resolver":"https://pith.science/pith/P3XEWQ2NC6C5OCRUPMJZ7SCFOK","bundle":"https://pith.science/pith/P3XEWQ2NC6C5OCRUPMJZ7SCFOK/bundle.json","state":"https://pith.science/pith/P3XEWQ2NC6C5OCRUPMJZ7SCFOK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P3XEWQ2NC6C5OCRUPMJZ7SCFOK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:P3XEWQ2NC6C5OCRUPMJZ7SCFOK","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":"fd2116d431f835ceda6de7eddeccc29b3f1b047bb65224b68f822fb2d4bb1c44","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2020-03-09T07:25:54Z","title_canon_sha256":"af77b928fd204e3b7ed9ab8f7f39c0780fee020980e008b3bce319e3e77eecd2"},"schema_version":"1.0","source":{"id":"2003.03952","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2003.03952","created_at":"2026-07-05T00:57:18Z"},{"alias_kind":"arxiv_version","alias_value":"2003.03952v1","created_at":"2026-07-05T00:57:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2003.03952","created_at":"2026-07-05T00:57:18Z"},{"alias_kind":"pith_short_12","alias_value":"P3XEWQ2NC6C5","created_at":"2026-07-05T00:57:18Z"},{"alias_kind":"pith_short_16","alias_value":"P3XEWQ2NC6C5OCRU","created_at":"2026-07-05T00:57:18Z"},{"alias_kind":"pith_short_8","alias_value":"P3XEWQ2N","created_at":"2026-07-05T00:57:18Z"}],"graph_snapshots":[{"event_id":"sha256:1f7055acae7944b86856bf94b5bf64efbabdb1a456f3f7f0a0a38cc7cb4383fc","target":"graph","created_at":"2026-07-05T00:57:18Z","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/2003.03952/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Two strategies for constructing general geometric operators in all dimensional loop quantum gravity are proposed. The different constructions are mainly come from the two different regularization methods for the de-densitized dual momentum, which play the role of building block for the spatial geometry. The first regularization method is a generalization of the regularization of the length operator in standard $(1+3)$-dimensional loop quantum gravity, while the second method is a natural extension of those for standard (D-1)-area and D-volume operators. Two versions of general geometric operat","authors_text":"Gaoping Long, Yongge Ma","cross_cats":["quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2020-03-09T07:25:54Z","title":"General geometric operators in all dimensional loop quantum gravity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2003.03952","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":"sha256:77d410c938a0b33bbf21402db277de1d88719ad14f04ee6d036635ec43244f83","target":"record","created_at":"2026-07-05T00:57:18Z","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":"fd2116d431f835ceda6de7eddeccc29b3f1b047bb65224b68f822fb2d4bb1c44","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2020-03-09T07:25:54Z","title_canon_sha256":"af77b928fd204e3b7ed9ab8f7f39c0780fee020980e008b3bce319e3e77eecd2"},"schema_version":"1.0","source":{"id":"2003.03952","kind":"arxiv","version":1}},"canonical_sha256":"7eee4b434d1785d70a347b139fc84572841b014b87fd7cb10d89bbe60848f8a9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7eee4b434d1785d70a347b139fc84572841b014b87fd7cb10d89bbe60848f8a9","first_computed_at":"2026-07-05T00:57:18.951274Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:57:18.951274Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kGjW2N1xtM4pXSvzqMsj/ZtDJkodOJaNbbG1ifGfXI+5HFSsJM6ENWDtFc/HAgSE12yKP/Mqa2Mj3AwHstJTDg==","signature_status":"signed_v1","signed_at":"2026-07-05T00:57:18.951710Z","signed_message":"canonical_sha256_bytes"},"source_id":"2003.03952","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:77d410c938a0b33bbf21402db277de1d88719ad14f04ee6d036635ec43244f83","sha256:1f7055acae7944b86856bf94b5bf64efbabdb1a456f3f7f0a0a38cc7cb4383fc"],"state_sha256":"5a558249d9fa9d12c13777090bcd184087687bc289ef8f52e8e0dbdc1b3c76ea"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XFmngz/OPD6C768GblKKRrs33agZehsBi6NA0pN5dwcYbOUHmkRdda63FqDd/7uTf+tT9ye+sIxu5+cPUlibBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T12:39:26.977861Z","bundle_sha256":"35e98850f6d9bdf145a9b29bdc402ff95b97398b9d734228a8e4231ae4333eff"}}