{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:H4EBPYZZQS7EYKSVPGJ2G74QRK","short_pith_number":"pith:H4EBPYZZ","canonical_record":{"source":{"id":"1710.00221","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-09-30T16:29:24Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"5bd98c2ee92cb4a84ff40ad193a96ee1d746a5b1b41b5b5952dcabe31c531c18","abstract_canon_sha256":"a384772595f090d66517d78d936df8fa8f950bb76c08a3c09e70ab320bbd4401"},"schema_version":"1.0"},"canonical_sha256":"3f0817e33984be4c2a557993a37f908a89f61a0079b97bbcffe4445a5ff272d3","source":{"kind":"arxiv","id":"1710.00221","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.00221","created_at":"2026-05-18T00:29:59Z"},{"alias_kind":"arxiv_version","alias_value":"1710.00221v1","created_at":"2026-05-18T00:29:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.00221","created_at":"2026-05-18T00:29:59Z"},{"alias_kind":"pith_short_12","alias_value":"H4EBPYZZQS7E","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"H4EBPYZZQS7EYKSV","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"H4EBPYZZ","created_at":"2026-05-18T12:31:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:H4EBPYZZQS7EYKSVPGJ2G74QRK","target":"record","payload":{"canonical_record":{"source":{"id":"1710.00221","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-09-30T16:29:24Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"5bd98c2ee92cb4a84ff40ad193a96ee1d746a5b1b41b5b5952dcabe31c531c18","abstract_canon_sha256":"a384772595f090d66517d78d936df8fa8f950bb76c08a3c09e70ab320bbd4401"},"schema_version":"1.0"},"canonical_sha256":"3f0817e33984be4c2a557993a37f908a89f61a0079b97bbcffe4445a5ff272d3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:59.675439Z","signature_b64":"zW24y7FLLe1w/Jo1r4JiVGMn4vIcxSyOZCL2C157uHlErUw6BKvox48H/DNlyzVqtCK4CRUaNNAP04dtarMHCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3f0817e33984be4c2a557993a37f908a89f61a0079b97bbcffe4445a5ff272d3","last_reissued_at":"2026-05-18T00:29:59.675032Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:59.675032Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.00221","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":"2026-05-18T00:29:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QiTg8k1kxV8Hism6xItdbucz8jnVhTmOtVcaiRfpVQduF488NoLQOgOv8sE04b4FX/ExjddxbHH/+BnBMTP0Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T08:42:50.365761Z"},"content_sha256":"63b289ea8180fc12616557e8b69ea883d9f5e30c787d01622005e8c79e5f480f","schema_version":"1.0","event_id":"sha256:63b289ea8180fc12616557e8b69ea883d9f5e30c787d01622005e8c79e5f480f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:H4EBPYZZQS7EYKSVPGJ2G74QRK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Topological Network Entanglement as Order Parameter for the Emergence of Geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"hep-th","authors_text":"C. A. Trugenberger, M. C. Diamantini","submitted_at":"2017-09-30T16:29:24Z","abstract_excerpt":"We show that, in discrete models of quantum gravity, emergent geometric space can be viewed as the entanglement pattern in a mixed quantum state of the \"universe\", characterized by a universal topological network entanglement. As a concrete example we analyze the recently proposed model in which geometry emerges due to the condensation of 4-cycles in random regular bipartite graphs, driven by the combinatorial Ollivier-Ricci curvature. Using this model we show that the emergence of geometric order decreases the entanglement entropy of random configurations. The lowest geometric entanglement en"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.00221","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":"2026-05-18T00:29:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UJ017hQeECVZB3Re+R7nA08wBESEO3zSy7U0yU4py80cmrPBldFX+zam+QxW63FopJHVcHXHhDRKnRqVCwo7Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T08:42:50.366120Z"},"content_sha256":"b60bf9064c59fd0531ab8470a775a725fb343fec87b2a12511121acbc5c9e85f","schema_version":"1.0","event_id":"sha256:b60bf9064c59fd0531ab8470a775a725fb343fec87b2a12511121acbc5c9e85f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H4EBPYZZQS7EYKSVPGJ2G74QRK/bundle.json","state_url":"https://pith.science/pith/H4EBPYZZQS7EYKSVPGJ2G74QRK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H4EBPYZZQS7EYKSVPGJ2G74QRK/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":"2026-06-04T08:42:50Z","links":{"resolver":"https://pith.science/pith/H4EBPYZZQS7EYKSVPGJ2G74QRK","bundle":"https://pith.science/pith/H4EBPYZZQS7EYKSVPGJ2G74QRK/bundle.json","state":"https://pith.science/pith/H4EBPYZZQS7EYKSVPGJ2G74QRK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H4EBPYZZQS7EYKSVPGJ2G74QRK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:H4EBPYZZQS7EYKSVPGJ2G74QRK","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":"a384772595f090d66517d78d936df8fa8f950bb76c08a3c09e70ab320bbd4401","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-09-30T16:29:24Z","title_canon_sha256":"5bd98c2ee92cb4a84ff40ad193a96ee1d746a5b1b41b5b5952dcabe31c531c18"},"schema_version":"1.0","source":{"id":"1710.00221","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.00221","created_at":"2026-05-18T00:29:59Z"},{"alias_kind":"arxiv_version","alias_value":"1710.00221v1","created_at":"2026-05-18T00:29:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.00221","created_at":"2026-05-18T00:29:59Z"},{"alias_kind":"pith_short_12","alias_value":"H4EBPYZZQS7E","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"H4EBPYZZQS7EYKSV","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"H4EBPYZZ","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:b60bf9064c59fd0531ab8470a775a725fb343fec87b2a12511121acbc5c9e85f","target":"graph","created_at":"2026-05-18T00:29:59Z","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 show that, in discrete models of quantum gravity, emergent geometric space can be viewed as the entanglement pattern in a mixed quantum state of the \"universe\", characterized by a universal topological network entanglement. As a concrete example we analyze the recently proposed model in which geometry emerges due to the condensation of 4-cycles in random regular bipartite graphs, driven by the combinatorial Ollivier-Ricci curvature. Using this model we show that the emergence of geometric order decreases the entanglement entropy of random configurations. The lowest geometric entanglement en","authors_text":"C. A. Trugenberger, M. C. Diamantini","cross_cats":["gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-09-30T16:29:24Z","title":"Topological Network Entanglement as Order Parameter for the Emergence of Geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.00221","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":"sha256:63b289ea8180fc12616557e8b69ea883d9f5e30c787d01622005e8c79e5f480f","target":"record","created_at":"2026-05-18T00:29:59Z","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":"a384772595f090d66517d78d936df8fa8f950bb76c08a3c09e70ab320bbd4401","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-09-30T16:29:24Z","title_canon_sha256":"5bd98c2ee92cb4a84ff40ad193a96ee1d746a5b1b41b5b5952dcabe31c531c18"},"schema_version":"1.0","source":{"id":"1710.00221","kind":"arxiv","version":1}},"canonical_sha256":"3f0817e33984be4c2a557993a37f908a89f61a0079b97bbcffe4445a5ff272d3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3f0817e33984be4c2a557993a37f908a89f61a0079b97bbcffe4445a5ff272d3","first_computed_at":"2026-05-18T00:29:59.675032Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:59.675032Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zW24y7FLLe1w/Jo1r4JiVGMn4vIcxSyOZCL2C157uHlErUw6BKvox48H/DNlyzVqtCK4CRUaNNAP04dtarMHCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:59.675439Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.00221","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:63b289ea8180fc12616557e8b69ea883d9f5e30c787d01622005e8c79e5f480f","sha256:b60bf9064c59fd0531ab8470a775a725fb343fec87b2a12511121acbc5c9e85f"],"state_sha256":"900e0fba4dc3e9d82d58f2244258e7120a6b7fb3e8a5c9c167ff2ceb449c725b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XoHBO5Twc0J6LZPr1t0vVbJuncbC7eu6deIPYnKOkMOwXGcsZqvJrRyr99GYbNId43XkjDcgBdDfBC7XxSD7Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T08:42:50.368287Z","bundle_sha256":"55407eb4d34e890f3e7659407d69b853dc56d0e6c8da0cb15e6b607e7f3ae25d"}}