{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:TDTWJAUKCJOWWSVWSMYGB2EYLA","short_pith_number":"pith:TDTWJAUK","canonical_record":{"source":{"id":"1606.01830","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2016-06-06T17:09:40Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"60308a8318dafbbea9211e5591d7a135f3cc8feec2991e16a44eb77b39855471","abstract_canon_sha256":"3a35a24ac4aec707084cc50572d2e752d797299688cd789793cfd159723b1c90"},"schema_version":"1.0"},"canonical_sha256":"98e764828a125d6b4ab6933060e89858288f1c9ad22a7031d7b9f9cebf5d8bf5","source":{"kind":"arxiv","id":"1606.01830","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.01830","created_at":"2026-05-18T00:10:14Z"},{"alias_kind":"arxiv_version","alias_value":"1606.01830v3","created_at":"2026-05-18T00:10:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.01830","created_at":"2026-05-18T00:10:14Z"},{"alias_kind":"pith_short_12","alias_value":"TDTWJAUKCJOW","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"TDTWJAUKCJOWWSVW","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"TDTWJAUK","created_at":"2026-05-18T12:30:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:TDTWJAUKCJOWWSVWSMYGB2EYLA","target":"record","payload":{"canonical_record":{"source":{"id":"1606.01830","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2016-06-06T17:09:40Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"60308a8318dafbbea9211e5591d7a135f3cc8feec2991e16a44eb77b39855471","abstract_canon_sha256":"3a35a24ac4aec707084cc50572d2e752d797299688cd789793cfd159723b1c90"},"schema_version":"1.0"},"canonical_sha256":"98e764828a125d6b4ab6933060e89858288f1c9ad22a7031d7b9f9cebf5d8bf5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:14.054748Z","signature_b64":"pUoQbN/sRYrHj88KGotIbKVshsKs9Xy4MT+yuk20ZGxuyvfkJkacIBxvbyiPSyd6T8ihkyjacnV5iyvaRnjbCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"98e764828a125d6b4ab6933060e89858288f1c9ad22a7031d7b9f9cebf5d8bf5","last_reissued_at":"2026-05-18T00:10:14.054021Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:14.054021Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.01830","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:10:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zLZEz9vuw2JOx824EEkiVXB70NgXutZs+tPz9NVQUo74v3tlRUbzqY43xKeE+dgwHwu5vlx0Bhc5+PB0kX7sAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T18:38:00.997300Z"},"content_sha256":"6d54d9eb94b622d817d29d66fe2336f5d35e5292f2350e3e697cbd54609433ec","schema_version":"1.0","event_id":"sha256:6d54d9eb94b622d817d29d66fe2336f5d35e5292f2350e3e697cbd54609433ec"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:TDTWJAUKCJOWWSVWSMYGB2EYLA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exploring the Tomlin-Varadarajan quantum constraints in $U(1)^3$ loop quantum gravity: solutions and the Minkowski theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"gr-qc","authors_text":"Chun-Yen Lin, Jerzy lewandowski","submitted_at":"2016-06-06T17:09:40Z","abstract_excerpt":"We explicitly solved the anomaly-free quantum constraints proposed by Tomlin and Varadarajan for the weak Euclidean model of canonical loop quantum gravity, in a large subspace of the model's kinematic Hilbert space which is the space of the charge network states. In doing so, we first identified the subspace on which each of the constraints acts convergingly, and then by explicitly evaluating such actions we found the complete set of the solutions in the identified subspace. We showed that the space of solutions consists of two classes of states, with the first class having a property that in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.01830","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:10:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WHpGVVWbwsZ1jqyB36tcLYACcGAESlUNezdce0GmqNdr48fEhVWy+gEo03MarEAFb41rzu9XxZhMu0IP6EyxCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T18:38:00.997981Z"},"content_sha256":"f6e22860e1935c44ad22d00c20d1aae21b487cabe11bb15d1f5ebf0e9f061c11","schema_version":"1.0","event_id":"sha256:f6e22860e1935c44ad22d00c20d1aae21b487cabe11bb15d1f5ebf0e9f061c11"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TDTWJAUKCJOWWSVWSMYGB2EYLA/bundle.json","state_url":"https://pith.science/pith/TDTWJAUKCJOWWSVWSMYGB2EYLA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TDTWJAUKCJOWWSVWSMYGB2EYLA/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":"2026-05-29T18:38:00Z","links":{"resolver":"https://pith.science/pith/TDTWJAUKCJOWWSVWSMYGB2EYLA","bundle":"https://pith.science/pith/TDTWJAUKCJOWWSVWSMYGB2EYLA/bundle.json","state":"https://pith.science/pith/TDTWJAUKCJOWWSVWSMYGB2EYLA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TDTWJAUKCJOWWSVWSMYGB2EYLA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:TDTWJAUKCJOWWSVWSMYGB2EYLA","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":"3a35a24ac4aec707084cc50572d2e752d797299688cd789793cfd159723b1c90","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2016-06-06T17:09:40Z","title_canon_sha256":"60308a8318dafbbea9211e5591d7a135f3cc8feec2991e16a44eb77b39855471"},"schema_version":"1.0","source":{"id":"1606.01830","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.01830","created_at":"2026-05-18T00:10:14Z"},{"alias_kind":"arxiv_version","alias_value":"1606.01830v3","created_at":"2026-05-18T00:10:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.01830","created_at":"2026-05-18T00:10:14Z"},{"alias_kind":"pith_short_12","alias_value":"TDTWJAUKCJOW","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"TDTWJAUKCJOWWSVW","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"TDTWJAUK","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:f6e22860e1935c44ad22d00c20d1aae21b487cabe11bb15d1f5ebf0e9f061c11","target":"graph","created_at":"2026-05-18T00:10:14Z","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":"We explicitly solved the anomaly-free quantum constraints proposed by Tomlin and Varadarajan for the weak Euclidean model of canonical loop quantum gravity, in a large subspace of the model's kinematic Hilbert space which is the space of the charge network states. In doing so, we first identified the subspace on which each of the constraints acts convergingly, and then by explicitly evaluating such actions we found the complete set of the solutions in the identified subspace. We showed that the space of solutions consists of two classes of states, with the first class having a property that in","authors_text":"Chun-Yen Lin, Jerzy lewandowski","cross_cats":["hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2016-06-06T17:09:40Z","title":"Exploring the Tomlin-Varadarajan quantum constraints in $U(1)^3$ loop quantum gravity: solutions and the Minkowski theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.01830","kind":"arxiv","version":3},"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":"sha256:6d54d9eb94b622d817d29d66fe2336f5d35e5292f2350e3e697cbd54609433ec","target":"record","created_at":"2026-05-18T00:10:14Z","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":"3a35a24ac4aec707084cc50572d2e752d797299688cd789793cfd159723b1c90","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2016-06-06T17:09:40Z","title_canon_sha256":"60308a8318dafbbea9211e5591d7a135f3cc8feec2991e16a44eb77b39855471"},"schema_version":"1.0","source":{"id":"1606.01830","kind":"arxiv","version":3}},"canonical_sha256":"98e764828a125d6b4ab6933060e89858288f1c9ad22a7031d7b9f9cebf5d8bf5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"98e764828a125d6b4ab6933060e89858288f1c9ad22a7031d7b9f9cebf5d8bf5","first_computed_at":"2026-05-18T00:10:14.054021Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:14.054021Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pUoQbN/sRYrHj88KGotIbKVshsKs9Xy4MT+yuk20ZGxuyvfkJkacIBxvbyiPSyd6T8ihkyjacnV5iyvaRnjbCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:14.054748Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.01830","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d54d9eb94b622d817d29d66fe2336f5d35e5292f2350e3e697cbd54609433ec","sha256:f6e22860e1935c44ad22d00c20d1aae21b487cabe11bb15d1f5ebf0e9f061c11"],"state_sha256":"fa690b17373e595d8f381266444224af6699e70b9163e7ffe766353dbe2bdb3f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"65q0OsjneAfryVDZ9dXaDSS1Hze3qtY5ngXHdXC07FYOs2h6KuYkERShGnqVuoHSgNa9awOic3a753qj3TJiDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T18:38:01.001488Z","bundle_sha256":"5af902720093d5d17b7b282d0324a5e95e252e7ea90526351232aa32daea7486"}}