{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1997:YFXROMNLTFDP6ABEXYHTHQ4KOZ","short_pith_number":"pith:YFXROMNL","canonical_record":{"source":{"id":"hep-th/9711162","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1997-11-20T21:21:36Z","cross_cats_sorted":[],"title_canon_sha256":"71b015fbb68f525dbcb79c740d6a9474a1b1f2386313b130ecf14598eb7a6b86","abstract_canon_sha256":"8f8aa9851b769919e00e949ae43b713b9a1681587e55651eb9a2702ac414e56b"},"schema_version":"1.0"},"canonical_sha256":"c16f1731ab9946ff0024be0f33c38a76583fe16dce9647320b033149ae409247","source":{"kind":"arxiv","id":"hep-th/9711162","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9711162","created_at":"2026-05-18T04:35:16Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9711162v2","created_at":"2026-05-18T04:35:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9711162","created_at":"2026-05-18T04:35:16Z"},{"alias_kind":"pith_short_12","alias_value":"YFXROMNLTFDP","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_16","alias_value":"YFXROMNLTFDP6ABE","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_8","alias_value":"YFXROMNL","created_at":"2026-05-18T12:25:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1997:YFXROMNLTFDP6ABEXYHTHQ4KOZ","target":"record","payload":{"canonical_record":{"source":{"id":"hep-th/9711162","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1997-11-20T21:21:36Z","cross_cats_sorted":[],"title_canon_sha256":"71b015fbb68f525dbcb79c740d6a9474a1b1f2386313b130ecf14598eb7a6b86","abstract_canon_sha256":"8f8aa9851b769919e00e949ae43b713b9a1681587e55651eb9a2702ac414e56b"},"schema_version":"1.0"},"canonical_sha256":"c16f1731ab9946ff0024be0f33c38a76583fe16dce9647320b033149ae409247","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:35:16.060624Z","signature_b64":"Ilcavf19psz+qsvtgJ9EB3HlPfIULHdy0V/eEKCJlt4UAVA9vLqH+2WjJl0Blnd8YrmJAz1XcIzCakB2ZBUVAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c16f1731ab9946ff0024be0f33c38a76583fe16dce9647320b033149ae409247","last_reissued_at":"2026-05-18T04:35:16.060121Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:35:16.060121Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"hep-th/9711162","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:35:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yw2b6r0ZCR15MI7/tW1ulA4eAEYBtfoIUtKswOR+pdrQxqfOP25PJyzCtrlJE/YgFiWna80jnD0jcCWvrzK4Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T22:16:06.396121Z"},"content_sha256":"cb5847022e6ca86ff5ca173fcb8a93a1cec1ee5d42dc7e61c7fea29d060fbd38","schema_version":"1.0","event_id":"sha256:cb5847022e6ca86ff5ca173fcb8a93a1cec1ee5d42dc7e61c7fea29d060fbd38"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1997:YFXROMNLTFDP6ABEXYHTHQ4KOZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Noncommutative Geometry and Matrix Theory: Compactification on Tori","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Alain Connes, Albert Schwarz, Michael R. Douglas","submitted_at":"1997-11-20T21:21:36Z","abstract_excerpt":"We study toroidal compactification of Matrix theory, using ideas and results of non-commutative geometry. We generalize this to compactification on the noncommutative torus, explain the classification of these backgrounds, and argue that they correspond in supergravity to tori with constant background three-form tensor field. The paper includes an introduction for mathematicians to the IKKT formulation of Matrix theory and its relation to the BFSS Matrix theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9711162","kind":"arxiv","version":2},"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":"2026-05-18T04:35:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5fArXjVW3ZQZPuLutcLfZQBsolOoLeVDCsjFgCbh3ix3/9RkbmqL5/wsyzRjHfuTNInWaInVaJnTzYthnS6hBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T22:16:06.396580Z"},"content_sha256":"515ecb71b999ab7e98fdcd01e45957640cb1782abd19840d849eb6e186457966","schema_version":"1.0","event_id":"sha256:515ecb71b999ab7e98fdcd01e45957640cb1782abd19840d849eb6e186457966"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YFXROMNLTFDP6ABEXYHTHQ4KOZ/bundle.json","state_url":"https://pith.science/pith/YFXROMNLTFDP6ABEXYHTHQ4KOZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YFXROMNLTFDP6ABEXYHTHQ4KOZ/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":"2026-05-25T22:16:06Z","links":{"resolver":"https://pith.science/pith/YFXROMNLTFDP6ABEXYHTHQ4KOZ","bundle":"https://pith.science/pith/YFXROMNLTFDP6ABEXYHTHQ4KOZ/bundle.json","state":"https://pith.science/pith/YFXROMNLTFDP6ABEXYHTHQ4KOZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YFXROMNLTFDP6ABEXYHTHQ4KOZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1997:YFXROMNLTFDP6ABEXYHTHQ4KOZ","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":"8f8aa9851b769919e00e949ae43b713b9a1681587e55651eb9a2702ac414e56b","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"1997-11-20T21:21:36Z","title_canon_sha256":"71b015fbb68f525dbcb79c740d6a9474a1b1f2386313b130ecf14598eb7a6b86"},"schema_version":"1.0","source":{"id":"hep-th/9711162","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9711162","created_at":"2026-05-18T04:35:16Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9711162v2","created_at":"2026-05-18T04:35:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9711162","created_at":"2026-05-18T04:35:16Z"},{"alias_kind":"pith_short_12","alias_value":"YFXROMNLTFDP","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_16","alias_value":"YFXROMNLTFDP6ABE","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_8","alias_value":"YFXROMNL","created_at":"2026-05-18T12:25:48Z"}],"graph_snapshots":[{"event_id":"sha256:515ecb71b999ab7e98fdcd01e45957640cb1782abd19840d849eb6e186457966","target":"graph","created_at":"2026-05-18T04:35:16Z","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 study toroidal compactification of Matrix theory, using ideas and results of non-commutative geometry. We generalize this to compactification on the noncommutative torus, explain the classification of these backgrounds, and argue that they correspond in supergravity to tori with constant background three-form tensor field. The paper includes an introduction for mathematicians to the IKKT formulation of Matrix theory and its relation to the BFSS Matrix theory.","authors_text":"Alain Connes, Albert Schwarz, Michael R. Douglas","cross_cats":[],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"1997-11-20T21:21:36Z","title":"Noncommutative Geometry and Matrix Theory: Compactification on Tori"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9711162","kind":"arxiv","version":2},"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:cb5847022e6ca86ff5ca173fcb8a93a1cec1ee5d42dc7e61c7fea29d060fbd38","target":"record","created_at":"2026-05-18T04:35:16Z","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":"8f8aa9851b769919e00e949ae43b713b9a1681587e55651eb9a2702ac414e56b","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"1997-11-20T21:21:36Z","title_canon_sha256":"71b015fbb68f525dbcb79c740d6a9474a1b1f2386313b130ecf14598eb7a6b86"},"schema_version":"1.0","source":{"id":"hep-th/9711162","kind":"arxiv","version":2}},"canonical_sha256":"c16f1731ab9946ff0024be0f33c38a76583fe16dce9647320b033149ae409247","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c16f1731ab9946ff0024be0f33c38a76583fe16dce9647320b033149ae409247","first_computed_at":"2026-05-18T04:35:16.060121Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:35:16.060121Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ilcavf19psz+qsvtgJ9EB3HlPfIULHdy0V/eEKCJlt4UAVA9vLqH+2WjJl0Blnd8YrmJAz1XcIzCakB2ZBUVAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:35:16.060624Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/9711162","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cb5847022e6ca86ff5ca173fcb8a93a1cec1ee5d42dc7e61c7fea29d060fbd38","sha256:515ecb71b999ab7e98fdcd01e45957640cb1782abd19840d849eb6e186457966"],"state_sha256":"528cba5d373fa14e3217fd6487cfc2eb9bd723bf3b63dd34e89008c9720eb8b2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"04JB1NBZanWuunQgwwlDdKvADUVgpFqBv9Dbp/1DwPpxd3XTNTplizcF9iqaiGKtrtIbxRMcyO/nnbky9xL/AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T22:16:06.400049Z","bundle_sha256":"9c20641aa91d3ddb8ef2636297170b49c9d6c420efd71faf94416e77c2bbd127"}}