{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:33AFGBCOLJ5DNSHQ3KXEC2C4PT","short_pith_number":"pith:33AFGBCO","canonical_record":{"source":{"id":"2102.12023","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-02-24T02:03:54Z","cross_cats_sorted":["cond-mat.str-el","gr-qc","math-ph","math.MP","quant-ph"],"title_canon_sha256":"90b1b3d9eb22e4cb49367c851e07e658a2a986b93d2eea377caa862809829be5","abstract_canon_sha256":"8f6c6e3b1f6618012c81acda14f711056a63c6d12f6ed7f839f9182cf1632096"},"schema_version":"1.0"},"canonical_sha256":"dec053044e5a7a36c8f0daae41685c7ce8e5a720ec73ecc6f53c1347a8a29e01","source":{"kind":"arxiv","id":"2102.12023","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.12023","created_at":"2026-07-05T02:53:36Z"},{"alias_kind":"arxiv_version","alias_value":"2102.12023v3","created_at":"2026-07-05T02:53:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.12023","created_at":"2026-07-05T02:53:36Z"},{"alias_kind":"pith_short_12","alias_value":"33AFGBCOLJ5D","created_at":"2026-07-05T02:53:36Z"},{"alias_kind":"pith_short_16","alias_value":"33AFGBCOLJ5DNSHQ","created_at":"2026-07-05T02:53:36Z"},{"alias_kind":"pith_short_8","alias_value":"33AFGBCO","created_at":"2026-07-05T02:53:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:33AFGBCOLJ5DNSHQ3KXEC2C4PT","target":"record","payload":{"canonical_record":{"source":{"id":"2102.12023","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-02-24T02:03:54Z","cross_cats_sorted":["cond-mat.str-el","gr-qc","math-ph","math.MP","quant-ph"],"title_canon_sha256":"90b1b3d9eb22e4cb49367c851e07e658a2a986b93d2eea377caa862809829be5","abstract_canon_sha256":"8f6c6e3b1f6618012c81acda14f711056a63c6d12f6ed7f839f9182cf1632096"},"schema_version":"1.0"},"canonical_sha256":"dec053044e5a7a36c8f0daae41685c7ce8e5a720ec73ecc6f53c1347a8a29e01","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:53:36.290297Z","signature_b64":"0JiL/ug2EsqifNzWd8z/nhcCjgD6Us0Pobiy8YUKZJTE/WjwpgieWvSN9Lxvqvy3XiXiIGZ8fdPKt1MO5Uo9BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dec053044e5a7a36c8f0daae41685c7ce8e5a720ec73ecc6f53c1347a8a29e01","last_reissued_at":"2026-07-05T02:53:36.289727Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:53:36.289727Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2102.12023","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":"2026-07-05T02:53:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HTrR7n3X7ogsy1KL7qFhKb0jEcfrSLKnJtBYeywoN36P9oP3fqGkcxFfV8Y+1KSLHVnDKy//k+x5bxkc9/VOBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T12:37:59.782814Z"},"content_sha256":"2bf3df71038822d02b72aab79e8151d59ed542108b5f1ba2567a91c108de3d5c","schema_version":"1.0","event_id":"sha256:2bf3df71038822d02b72aab79e8151d59ed542108b5f1ba2567a91c108de3d5c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:33AFGBCOLJ5DNSHQ3KXEC2C4PT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bending the Bruhat-Tits Tree I:Tensor Network and Emergent Einstein Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.str-el","gr-qc","math-ph","math.MP","quant-ph"],"primary_cat":"hep-th","authors_text":"Lin Chen, Ling-Yan Hung, Xirong Liu","submitted_at":"2021-02-24T02:03:54Z","abstract_excerpt":"As an extended companion paper to [1], we elaborate in detail how the tensor network construction of a p-adic CFT encodes geometric information of a dual geometry even as we deform the CFT away from the fixed point by finding a way to assign distances to the tensor network. In fact we demonstrate that a unique (up to normalizations) emergent graph Einstein equation is satisfied by the geometric data encoded in the tensor network, and the graph Einstein tensor automatically recovers the known proposal in the mathematics literature, at least perturbatively order by order in the deformation away "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.12023","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2102.12023/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":"2026-07-05T02:53:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TLIvGAxzAsi8OOhGcqlnoJY4l+5VOirHw9SdY0zWlf7+nwNhfEZgkv5Sk2xteLJQO6iI3vBFiT9P42GfTFz3Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T12:37:59.783494Z"},"content_sha256":"ea0b7b660660bdc99114d3b0586ea2f11f19d8ad17360871cd3805e706d4fddf","schema_version":"1.0","event_id":"sha256:ea0b7b660660bdc99114d3b0586ea2f11f19d8ad17360871cd3805e706d4fddf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/33AFGBCOLJ5DNSHQ3KXEC2C4PT/bundle.json","state_url":"https://pith.science/pith/33AFGBCOLJ5DNSHQ3KXEC2C4PT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/33AFGBCOLJ5DNSHQ3KXEC2C4PT/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":"2026-08-11T12:37:59Z","links":{"resolver":"https://pith.science/pith/33AFGBCOLJ5DNSHQ3KXEC2C4PT","bundle":"https://pith.science/pith/33AFGBCOLJ5DNSHQ3KXEC2C4PT/bundle.json","state":"https://pith.science/pith/33AFGBCOLJ5DNSHQ3KXEC2C4PT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/33AFGBCOLJ5DNSHQ3KXEC2C4PT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:33AFGBCOLJ5DNSHQ3KXEC2C4PT","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":"8f6c6e3b1f6618012c81acda14f711056a63c6d12f6ed7f839f9182cf1632096","cross_cats_sorted":["cond-mat.str-el","gr-qc","math-ph","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-02-24T02:03:54Z","title_canon_sha256":"90b1b3d9eb22e4cb49367c851e07e658a2a986b93d2eea377caa862809829be5"},"schema_version":"1.0","source":{"id":"2102.12023","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.12023","created_at":"2026-07-05T02:53:36Z"},{"alias_kind":"arxiv_version","alias_value":"2102.12023v3","created_at":"2026-07-05T02:53:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.12023","created_at":"2026-07-05T02:53:36Z"},{"alias_kind":"pith_short_12","alias_value":"33AFGBCOLJ5D","created_at":"2026-07-05T02:53:36Z"},{"alias_kind":"pith_short_16","alias_value":"33AFGBCOLJ5DNSHQ","created_at":"2026-07-05T02:53:36Z"},{"alias_kind":"pith_short_8","alias_value":"33AFGBCO","created_at":"2026-07-05T02:53:36Z"}],"graph_snapshots":[{"event_id":"sha256:ea0b7b660660bdc99114d3b0586ea2f11f19d8ad17360871cd3805e706d4fddf","target":"graph","created_at":"2026-07-05T02:53:36Z","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/2102.12023/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"As an extended companion paper to [1], we elaborate in detail how the tensor network construction of a p-adic CFT encodes geometric information of a dual geometry even as we deform the CFT away from the fixed point by finding a way to assign distances to the tensor network. In fact we demonstrate that a unique (up to normalizations) emergent graph Einstein equation is satisfied by the geometric data encoded in the tensor network, and the graph Einstein tensor automatically recovers the known proposal in the mathematics literature, at least perturbatively order by order in the deformation away ","authors_text":"Lin Chen, Ling-Yan Hung, Xirong Liu","cross_cats":["cond-mat.str-el","gr-qc","math-ph","math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-02-24T02:03:54Z","title":"Bending the Bruhat-Tits Tree I:Tensor Network and Emergent Einstein Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.12023","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":"sha256:2bf3df71038822d02b72aab79e8151d59ed542108b5f1ba2567a91c108de3d5c","target":"record","created_at":"2026-07-05T02:53:36Z","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":"8f6c6e3b1f6618012c81acda14f711056a63c6d12f6ed7f839f9182cf1632096","cross_cats_sorted":["cond-mat.str-el","gr-qc","math-ph","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-02-24T02:03:54Z","title_canon_sha256":"90b1b3d9eb22e4cb49367c851e07e658a2a986b93d2eea377caa862809829be5"},"schema_version":"1.0","source":{"id":"2102.12023","kind":"arxiv","version":3}},"canonical_sha256":"dec053044e5a7a36c8f0daae41685c7ce8e5a720ec73ecc6f53c1347a8a29e01","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dec053044e5a7a36c8f0daae41685c7ce8e5a720ec73ecc6f53c1347a8a29e01","first_computed_at":"2026-07-05T02:53:36.289727Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:53:36.289727Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0JiL/ug2EsqifNzWd8z/nhcCjgD6Us0Pobiy8YUKZJTE/WjwpgieWvSN9Lxvqvy3XiXiIGZ8fdPKt1MO5Uo9BQ==","signature_status":"signed_v1","signed_at":"2026-07-05T02:53:36.290297Z","signed_message":"canonical_sha256_bytes"},"source_id":"2102.12023","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2bf3df71038822d02b72aab79e8151d59ed542108b5f1ba2567a91c108de3d5c","sha256:ea0b7b660660bdc99114d3b0586ea2f11f19d8ad17360871cd3805e706d4fddf"],"state_sha256":"f67d82e573b87ee77815788b04677ab51c5a97e6591b7ec2aca7b1fce7e971c8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rSIPjpcYD+kRQviY5hyVdKHrRyG1TJUTMeJ50HQ0eroB/KBWYMClOhmstFxSI8Mppcr4zueVH2YIHbT3VdGZDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T12:37:59.788969Z","bundle_sha256":"0518a08d3ee67ee0929159b4a383d21171018b9a8d68c5bf98c7b4d0f61fbfd6"}}