{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:UHTWS25QWJ2D2FOK2CTE342PNE","short_pith_number":"pith:UHTWS25Q","canonical_record":{"source":{"id":"2605.13972","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2026-05-13T18:00:08Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"8574ef801ecd345fcfd59fb4ed121c9ba60775d573439ed4ec70450ebf3b81ba","abstract_canon_sha256":"c78776c9521d43df3008a6820b3f62ba67148a282b724a85d0621831b0d4c00c"},"schema_version":"1.0"},"canonical_sha256":"a1e7696bb0b2743d15cad0a64df34f692d3a51d0afe1b7bca1cfa04e299ebf57","source":{"kind":"arxiv","id":"2605.13972","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.13972","created_at":"2026-05-17T23:39:13Z"},{"alias_kind":"arxiv_version","alias_value":"2605.13972v1","created_at":"2026-05-17T23:39:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.13972","created_at":"2026-05-17T23:39:13Z"},{"alias_kind":"pith_short_12","alias_value":"UHTWS25QWJ2D","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"UHTWS25QWJ2D2FOK","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"UHTWS25Q","created_at":"2026-05-18T12:33:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:UHTWS25QWJ2D2FOK2CTE342PNE","target":"record","payload":{"canonical_record":{"source":{"id":"2605.13972","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2026-05-13T18:00:08Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"8574ef801ecd345fcfd59fb4ed121c9ba60775d573439ed4ec70450ebf3b81ba","abstract_canon_sha256":"c78776c9521d43df3008a6820b3f62ba67148a282b724a85d0621831b0d4c00c"},"schema_version":"1.0"},"canonical_sha256":"a1e7696bb0b2743d15cad0a64df34f692d3a51d0afe1b7bca1cfa04e299ebf57","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:13.483068Z","signature_b64":"DfCPRGXiCbogJNjgwbUC/yuCUONr09c9OPGiOaQ4iCij6NJgFIuajhdFiXYFb1PkNXC6ZtjXXZABhVeGjebyBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a1e7696bb0b2743d15cad0a64df34f692d3a51d0afe1b7bca1cfa04e299ebf57","last_reissued_at":"2026-05-17T23:39:13.482618Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:13.482618Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.13972","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":"2026-05-17T23:39:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z5UExSMlwo/vjyY5I334ICuW/Toi4uuTQHyOPKRobRS0rLafSmWA9esFFZrg+o39C8Pe+VFbVYoaaXOB/0DKCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T17:57:02.447147Z"},"content_sha256":"a4487895547ee0c20c9db25d9531d89dc8bcfa2645480ee6757f9010a6166d17","schema_version":"1.0","event_id":"sha256:a4487895547ee0c20c9db25d9531d89dc8bcfa2645480ee6757f9010a6166d17"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:UHTWS25QWJ2D2FOK2CTE342PNE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multi-Matrix Quantum Mechanics, Collective Fields and Emergent Space","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Bosonic multi-matrix quantum mechanics reduces to a collective field whose effective Hamiltonian has a stable vacuum.","cross_cats":["gr-qc"],"primary_cat":"hep-th","authors_text":"Robert Brandenberger, Suddhasattwa Brahma, Yue Lei","submitted_at":"2026-05-13T18:00:08Z","abstract_excerpt":"We study quantum mechanics of bosonic multi-matrix Lagragians in the collective field framework, with particular emphasis on three matrix models. We derive the effective Hamiltonian of the collective field and study the vacuum solution and its stability."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We derive the effective Hamiltonian of the collective field and study the vacuum solution and its stability.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The collective field framework can be directly applied to bosonic multi-matrix Lagrangians to produce a well-defined effective Hamiltonian whose vacuum is stable.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Derives the effective Hamiltonian in the collective field framework for three-matrix quantum mechanics models and analyzes the stability of the vacuum solution.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Bosonic multi-matrix quantum mechanics reduces to a collective field whose effective Hamiltonian has a stable vacuum.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"9477423697d153cafcc650090ab461364dadc76d53451d6156d8a6924035e526"},"source":{"id":"2605.13972","kind":"arxiv","version":1},"verdict":{"id":"4c0b29f8-43fd-423e-914b-d8c838c4b19d","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T02:25:13.739787Z","strongest_claim":"We derive the effective Hamiltonian of the collective field and study the vacuum solution and its stability.","one_line_summary":"Derives the effective Hamiltonian in the collective field framework for three-matrix quantum mechanics models and analyzes the stability of the vacuum solution.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The collective field framework can be directly applied to bosonic multi-matrix Lagrangians to produce a well-defined effective Hamiltonian whose vacuum is stable.","pith_extraction_headline":"Bosonic multi-matrix quantum mechanics reduces to a collective field whose effective Hamiltonian has a stable vacuum."},"references":{"count":28,"sample":[{"doi":"","year":1997,"title":"M Theory As A Matrix Model: A Conjecture","work_id":"ae12bcb1-76db-44db-b442-280a1a6d48f5","ref_index":1,"cited_arxiv_id":"hep-th/9610043","is_internal_anchor":true},{"doi":"","year":1997,"title":"A Large-N Reduced Model as Superstring","work_id":"a240509e-788c-4d54-9595-6e532b910ae2","ref_index":2,"cited_arxiv_id":"hep-th/9612115","is_internal_anchor":true},{"doi":"10.1103/physrevd.32.3228","year":1985,"title":"Constraints on Hamiltonian Lattice Formulations of Field Theories in an Expanding Universe,","work_id":"0ce082d8-6476-4c95-a994-89b65b1aecc1","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1393/ncc/i2022-22040-9","year":2020,"title":"Trans-Planckian Censorship and In- flationary Cosmology,","work_id":"b5c842ad-e19b-45a6-9692-fe342c626860","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2024,"title":"Regularization of Matrices in the Covariant Deriva- tive Interpretation of Matrix Models,","work_id":"2f6ced80-6df1-41b9-a063-0329c4ed7510","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":28,"snapshot_sha256":"9f327fa1924baa660a5af962eb94b6b8449e16a93f97fd29f822dce6a4ecb512","internal_anchors":8},"formal_canon":{"evidence_count":2,"snapshot_sha256":"5f9aec8fbba9e9c12f7d4be91b823566ce776a4d1833b43d04f99afb0a4a8103"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":"4c0b29f8-43fd-423e-914b-d8c838c4b19d"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:39:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"48JJCJ/mUNdVJAgtb1fXWGtiAaF/rcPDRL4oWpHiZ5adxd9BJSRv1nF3qLh8EFf4n0r8FYHBfn3GUEcfPUx0DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T17:57:02.447677Z"},"content_sha256":"ea22b298b45e91cf79065884d5882807e67ab2aed34d1925d60c4bb2b61aef6c","schema_version":"1.0","event_id":"sha256:ea22b298b45e91cf79065884d5882807e67ab2aed34d1925d60c4bb2b61aef6c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UHTWS25QWJ2D2FOK2CTE342PNE/bundle.json","state_url":"https://pith.science/pith/UHTWS25QWJ2D2FOK2CTE342PNE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UHTWS25QWJ2D2FOK2CTE342PNE/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":"2026-06-04T17:57:02Z","links":{"resolver":"https://pith.science/pith/UHTWS25QWJ2D2FOK2CTE342PNE","bundle":"https://pith.science/pith/UHTWS25QWJ2D2FOK2CTE342PNE/bundle.json","state":"https://pith.science/pith/UHTWS25QWJ2D2FOK2CTE342PNE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UHTWS25QWJ2D2FOK2CTE342PNE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:UHTWS25QWJ2D2FOK2CTE342PNE","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":"c78776c9521d43df3008a6820b3f62ba67148a282b724a85d0621831b0d4c00c","cross_cats_sorted":["gr-qc"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2026-05-13T18:00:08Z","title_canon_sha256":"8574ef801ecd345fcfd59fb4ed121c9ba60775d573439ed4ec70450ebf3b81ba"},"schema_version":"1.0","source":{"id":"2605.13972","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.13972","created_at":"2026-05-17T23:39:13Z"},{"alias_kind":"arxiv_version","alias_value":"2605.13972v1","created_at":"2026-05-17T23:39:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.13972","created_at":"2026-05-17T23:39:13Z"},{"alias_kind":"pith_short_12","alias_value":"UHTWS25QWJ2D","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"UHTWS25QWJ2D2FOK","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"UHTWS25Q","created_at":"2026-05-18T12:33:37Z"}],"graph_snapshots":[{"event_id":"sha256:ea22b298b45e91cf79065884d5882807e67ab2aed34d1925d60c4bb2b61aef6c","target":"graph","created_at":"2026-05-17T23:39:13Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"We derive the effective Hamiltonian of the collective field and study the vacuum solution and its stability."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The collective field framework can be directly applied to bosonic multi-matrix Lagrangians to produce a well-defined effective Hamiltonian whose vacuum is stable."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Derives the effective Hamiltonian in the collective field framework for three-matrix quantum mechanics models and analyzes the stability of the vacuum solution."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Bosonic multi-matrix quantum mechanics reduces to a collective field whose effective Hamiltonian has a stable vacuum."}],"snapshot_sha256":"9477423697d153cafcc650090ab461364dadc76d53451d6156d8a6924035e526"},"formal_canon":{"evidence_count":2,"snapshot_sha256":"5f9aec8fbba9e9c12f7d4be91b823566ce776a4d1833b43d04f99afb0a4a8103"},"paper":{"abstract_excerpt":"We study quantum mechanics of bosonic multi-matrix Lagragians in the collective field framework, with particular emphasis on three matrix models. We derive the effective Hamiltonian of the collective field and study the vacuum solution and its stability.","authors_text":"Robert Brandenberger, Suddhasattwa Brahma, Yue Lei","cross_cats":["gr-qc"],"headline":"Bosonic multi-matrix quantum mechanics reduces to a collective field whose effective Hamiltonian has a stable vacuum.","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2026-05-13T18:00:08Z","title":"Multi-Matrix Quantum Mechanics, Collective Fields and Emergent Space"},"references":{"count":28,"internal_anchors":8,"resolved_work":28,"sample":[{"cited_arxiv_id":"hep-th/9610043","doi":"","is_internal_anchor":true,"ref_index":1,"title":"M Theory As A Matrix Model: A Conjecture","work_id":"ae12bcb1-76db-44db-b442-280a1a6d48f5","year":1997},{"cited_arxiv_id":"hep-th/9612115","doi":"","is_internal_anchor":true,"ref_index":2,"title":"A Large-N Reduced Model as Superstring","work_id":"a240509e-788c-4d54-9595-6e532b910ae2","year":1997},{"cited_arxiv_id":"","doi":"10.1103/physrevd.32.3228","is_internal_anchor":false,"ref_index":3,"title":"Constraints on Hamiltonian Lattice Formulations of Field Theories in an Expanding Universe,","work_id":"0ce082d8-6476-4c95-a994-89b65b1aecc1","year":1985},{"cited_arxiv_id":"","doi":"10.1393/ncc/i2022-22040-9","is_internal_anchor":false,"ref_index":4,"title":"Trans-Planckian Censorship and In- flationary Cosmology,","work_id":"b5c842ad-e19b-45a6-9692-fe342c626860","year":2020},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"Regularization of Matrices in the Covariant Deriva- tive Interpretation of Matrix Models,","work_id":"2f6ced80-6df1-41b9-a063-0329c4ed7510","year":2024}],"snapshot_sha256":"9f327fa1924baa660a5af962eb94b6b8449e16a93f97fd29f822dce6a4ecb512"},"source":{"id":"2605.13972","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-15T02:25:13.739787Z","id":"4c0b29f8-43fd-423e-914b-d8c838c4b19d","model_set":{"reader":"grok-4.3"},"one_line_summary":"Derives the effective Hamiltonian in the collective field framework for three-matrix quantum mechanics models and analyzes the stability of the vacuum solution.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Bosonic multi-matrix quantum mechanics reduces to a collective field whose effective Hamiltonian has a stable vacuum.","strongest_claim":"We derive the effective Hamiltonian of the collective field and study the vacuum solution and its stability.","weakest_assumption":"The collective field framework can be directly applied to bosonic multi-matrix Lagrangians to produce a well-defined effective Hamiltonian whose vacuum is stable."}},"verdict_id":"4c0b29f8-43fd-423e-914b-d8c838c4b19d"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:a4487895547ee0c20c9db25d9531d89dc8bcfa2645480ee6757f9010a6166d17","target":"record","created_at":"2026-05-17T23:39:13Z","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":"c78776c9521d43df3008a6820b3f62ba67148a282b724a85d0621831b0d4c00c","cross_cats_sorted":["gr-qc"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2026-05-13T18:00:08Z","title_canon_sha256":"8574ef801ecd345fcfd59fb4ed121c9ba60775d573439ed4ec70450ebf3b81ba"},"schema_version":"1.0","source":{"id":"2605.13972","kind":"arxiv","version":1}},"canonical_sha256":"a1e7696bb0b2743d15cad0a64df34f692d3a51d0afe1b7bca1cfa04e299ebf57","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a1e7696bb0b2743d15cad0a64df34f692d3a51d0afe1b7bca1cfa04e299ebf57","first_computed_at":"2026-05-17T23:39:13.482618Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:39:13.482618Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DfCPRGXiCbogJNjgwbUC/yuCUONr09c9OPGiOaQ4iCij6NJgFIuajhdFiXYFb1PkNXC6ZtjXXZABhVeGjebyBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:39:13.483068Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.13972","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a4487895547ee0c20c9db25d9531d89dc8bcfa2645480ee6757f9010a6166d17","sha256:ea22b298b45e91cf79065884d5882807e67ab2aed34d1925d60c4bb2b61aef6c"],"state_sha256":"dad5ec9cf8b3fbfa6140e7240b806b66dc250a68a667418efbcc47ac4a709fee"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DN2JUDwm7SOrgvBL9dOT3cu5Vn58Z287mMh+T9efyL7lEi0WIzYQ679V7DN6nsKXIogEzcGoSwhzIokh8AALAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T17:57:02.450030Z","bundle_sha256":"b42c44ed54ded4ae3a1167b8f13ea5202174dc41f173ca6854042f43892a2534"}}