{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:ZMDQHWSSQVGZEX4CLXRYTIUAGS","short_pith_number":"pith:ZMDQHWSS","canonical_record":{"source":{"id":"1005.2130","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-05-12T15:34:41Z","cross_cats_sorted":["gr-qc","math-ph","math.MP","math.OA"],"title_canon_sha256":"0c96941ff5fe82368cc9feca1519ea2efefb1b2c4cddda8e4c2d8bcb4092d17d","abstract_canon_sha256":"1e0acf08eddf5074d0a1a4584608ef9dd20d87ae9b3a6aa250cd10c7fdd291e2"},"schema_version":"1.0"},"canonical_sha256":"cb0703da52854d925f825de389a2803488122db874870ff9bdbf08ed0a9905c4","source":{"kind":"arxiv","id":"1005.2130","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.2130","created_at":"2026-05-18T02:22:51Z"},{"alias_kind":"arxiv_version","alias_value":"1005.2130v1","created_at":"2026-05-18T02:22:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.2130","created_at":"2026-05-18T02:22:51Z"},{"alias_kind":"pith_short_12","alias_value":"ZMDQHWSSQVGZ","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"ZMDQHWSSQVGZEX4C","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"ZMDQHWSS","created_at":"2026-05-18T12:26:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:ZMDQHWSSQVGZEX4CLXRYTIUAGS","target":"record","payload":{"canonical_record":{"source":{"id":"1005.2130","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-05-12T15:34:41Z","cross_cats_sorted":["gr-qc","math-ph","math.MP","math.OA"],"title_canon_sha256":"0c96941ff5fe82368cc9feca1519ea2efefb1b2c4cddda8e4c2d8bcb4092d17d","abstract_canon_sha256":"1e0acf08eddf5074d0a1a4584608ef9dd20d87ae9b3a6aa250cd10c7fdd291e2"},"schema_version":"1.0"},"canonical_sha256":"cb0703da52854d925f825de389a2803488122db874870ff9bdbf08ed0a9905c4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:22:51.763662Z","signature_b64":"wAcuCNQDEI95MBjBgL+VMzCwLMl4VAOYLkkhEpgpP7Q65vgjwP8kfsvz5rh0yxyk1dF01QOprI7y02Lpd0QXBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cb0703da52854d925f825de389a2803488122db874870ff9bdbf08ed0a9905c4","last_reissued_at":"2026-05-18T02:22:51.763134Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:22:51.763134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1005.2130","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":"2026-05-18T02:22:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xz/GQgBxSh46v+SNqM9hD7PtSf3zWKbjKpCd315PgecyZPK2Pg9q2zOgzwnlFj+zYPRSe91e2k49wI/zOQkrCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T11:48:54.483705Z"},"content_sha256":"17bee20e8cd7c60e66a30953327a47fd4858aba30473cc569e73d9b76186bf41","schema_version":"1.0","event_id":"sha256:17bee20e8cd7c60e66a30953327a47fd4858aba30473cc569e73d9b76186bf41"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:ZMDQHWSSQVGZEX4CLXRYTIUAGS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum Geometry on Quantum Spacetime: Distance, Area and Volume Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","math-ph","math.MP","math.OA"],"primary_cat":"hep-th","authors_text":"Dorothea Bahns, Gherardo Piacitelli, Klaus Fredenhagen, Sergio Doplicher","submitted_at":"2010-05-12T15:34:41Z","abstract_excerpt":"We develop the first steps towards an analysis of geometry on the quantum spacetime proposed in [1]. The homogeneous elements of the universal differential algebra are naturally identified with operators living in tensor powers of Quantum Spacetime; this allows us to compute their spectra. In particular, we consider operators that can be interpreted as distances, areas, 3- and 4-volumes. The Minkowski distance operator between two independent events is shown to have pure Lebesgue spectrum with infinite multiplicity. The Euclidean distance operator is shown to have spectrum bounded below by a c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.2130","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":""},"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":"2026-05-18T02:22:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M4zlrMZanREmlNDJRFc0rzftpn6LxyPXrqdr3Q6xhW2LLg92hdj0itPYrYVqt/cAbcYHUQCr3vbUYUCQHe9oAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T11:48:54.484326Z"},"content_sha256":"96018a86b88c1a1423a606676eaef9a0d3c52ccfb34e732a8abf6c5c9186fbdb","schema_version":"1.0","event_id":"sha256:96018a86b88c1a1423a606676eaef9a0d3c52ccfb34e732a8abf6c5c9186fbdb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZMDQHWSSQVGZEX4CLXRYTIUAGS/bundle.json","state_url":"https://pith.science/pith/ZMDQHWSSQVGZEX4CLXRYTIUAGS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZMDQHWSSQVGZEX4CLXRYTIUAGS/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":"2026-05-22T11:48:54Z","links":{"resolver":"https://pith.science/pith/ZMDQHWSSQVGZEX4CLXRYTIUAGS","bundle":"https://pith.science/pith/ZMDQHWSSQVGZEX4CLXRYTIUAGS/bundle.json","state":"https://pith.science/pith/ZMDQHWSSQVGZEX4CLXRYTIUAGS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZMDQHWSSQVGZEX4CLXRYTIUAGS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:ZMDQHWSSQVGZEX4CLXRYTIUAGS","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":"1e0acf08eddf5074d0a1a4584608ef9dd20d87ae9b3a6aa250cd10c7fdd291e2","cross_cats_sorted":["gr-qc","math-ph","math.MP","math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-05-12T15:34:41Z","title_canon_sha256":"0c96941ff5fe82368cc9feca1519ea2efefb1b2c4cddda8e4c2d8bcb4092d17d"},"schema_version":"1.0","source":{"id":"1005.2130","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.2130","created_at":"2026-05-18T02:22:51Z"},{"alias_kind":"arxiv_version","alias_value":"1005.2130v1","created_at":"2026-05-18T02:22:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.2130","created_at":"2026-05-18T02:22:51Z"},{"alias_kind":"pith_short_12","alias_value":"ZMDQHWSSQVGZ","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"ZMDQHWSSQVGZEX4C","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"ZMDQHWSS","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:96018a86b88c1a1423a606676eaef9a0d3c52ccfb34e732a8abf6c5c9186fbdb","target":"graph","created_at":"2026-05-18T02:22:51Z","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 develop the first steps towards an analysis of geometry on the quantum spacetime proposed in [1]. The homogeneous elements of the universal differential algebra are naturally identified with operators living in tensor powers of Quantum Spacetime; this allows us to compute their spectra. In particular, we consider operators that can be interpreted as distances, areas, 3- and 4-volumes. The Minkowski distance operator between two independent events is shown to have pure Lebesgue spectrum with infinite multiplicity. The Euclidean distance operator is shown to have spectrum bounded below by a c","authors_text":"Dorothea Bahns, Gherardo Piacitelli, Klaus Fredenhagen, Sergio Doplicher","cross_cats":["gr-qc","math-ph","math.MP","math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-05-12T15:34:41Z","title":"Quantum Geometry on Quantum Spacetime: Distance, Area and Volume Operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.2130","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":"sha256:17bee20e8cd7c60e66a30953327a47fd4858aba30473cc569e73d9b76186bf41","target":"record","created_at":"2026-05-18T02:22:51Z","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":"1e0acf08eddf5074d0a1a4584608ef9dd20d87ae9b3a6aa250cd10c7fdd291e2","cross_cats_sorted":["gr-qc","math-ph","math.MP","math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-05-12T15:34:41Z","title_canon_sha256":"0c96941ff5fe82368cc9feca1519ea2efefb1b2c4cddda8e4c2d8bcb4092d17d"},"schema_version":"1.0","source":{"id":"1005.2130","kind":"arxiv","version":1}},"canonical_sha256":"cb0703da52854d925f825de389a2803488122db874870ff9bdbf08ed0a9905c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cb0703da52854d925f825de389a2803488122db874870ff9bdbf08ed0a9905c4","first_computed_at":"2026-05-18T02:22:51.763134Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:22:51.763134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wAcuCNQDEI95MBjBgL+VMzCwLMl4VAOYLkkhEpgpP7Q65vgjwP8kfsvz5rh0yxyk1dF01QOprI7y02Lpd0QXBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:22:51.763662Z","signed_message":"canonical_sha256_bytes"},"source_id":"1005.2130","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:17bee20e8cd7c60e66a30953327a47fd4858aba30473cc569e73d9b76186bf41","sha256:96018a86b88c1a1423a606676eaef9a0d3c52ccfb34e732a8abf6c5c9186fbdb"],"state_sha256":"3ef2c3c9f7226ddd9875e5732082f9c1de6741fa6243f5fd1c3df13ea16c6896"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HnEz9mfiXfhMDtiuk41+cjMJCKR4g/4VIzmiUTqrt6u0/6M47+uvSQup1Bb1aHV7GOpe7jyPTosgdyAwgMYfDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T11:48:54.487870Z","bundle_sha256":"28e53cd3e7610e7fda5ce7e3c53ec2a290e2a2e11aa90bfd367fe695db6c96ed"}}