{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:IDD5ZJRU2TSOXJU7RJTJVBGHYN","short_pith_number":"pith:IDD5ZJRU","canonical_record":{"source":{"id":"1412.0771","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-12-02T03:27:30Z","cross_cats_sorted":["math.AG","math.DG","math.SG"],"title_canon_sha256":"a7c1d93d60ebf596f77ad1eea6eaf45260c85ecc32dc08e0cc0ca2869c768de5","abstract_canon_sha256":"5765831f1a1888e901a301bfcc422c5ec5c08432f0be9265d36a5ce4041200c4"},"schema_version":"1.0"},"canonical_sha256":"40c7dca634d4e4eba69f8a669a84c7c367a925bbf968daae5de2935c64637a5a","source":{"kind":"arxiv","id":"1412.0771","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.0771","created_at":"2026-05-18T02:32:21Z"},{"alias_kind":"arxiv_version","alias_value":"1412.0771v1","created_at":"2026-05-18T02:32:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.0771","created_at":"2026-05-18T02:32:21Z"},{"alias_kind":"pith_short_12","alias_value":"IDD5ZJRU2TSO","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"IDD5ZJRU2TSOXJU7","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"IDD5ZJRU","created_at":"2026-05-18T12:28:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:IDD5ZJRU2TSOXJU7RJTJVBGHYN","target":"record","payload":{"canonical_record":{"source":{"id":"1412.0771","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-12-02T03:27:30Z","cross_cats_sorted":["math.AG","math.DG","math.SG"],"title_canon_sha256":"a7c1d93d60ebf596f77ad1eea6eaf45260c85ecc32dc08e0cc0ca2869c768de5","abstract_canon_sha256":"5765831f1a1888e901a301bfcc422c5ec5c08432f0be9265d36a5ce4041200c4"},"schema_version":"1.0"},"canonical_sha256":"40c7dca634d4e4eba69f8a669a84c7c367a925bbf968daae5de2935c64637a5a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:32:21.252163Z","signature_b64":"HJpxWsUY/kDqUk5Kp+yHozaIM6yIwzZ4TGP65sszGehbvWcSSy6r1qshxEQoESa4wHaiqLBue+C/aRaSi/H8CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"40c7dca634d4e4eba69f8a669a84c7c367a925bbf968daae5de2935c64637a5a","last_reissued_at":"2026-05-18T02:32:21.251782Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:32:21.251782Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.0771","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":"2026-05-18T02:32:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kGu9ujkLOIDH7CCJBm3x/Icf/wGlP9kkc5a6h0jsMx/DdQ9FDAR0hYTNyLYaEC5kJcjIQ99SRZDpe99RX3cXAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T12:08:33.568147Z"},"content_sha256":"ac0e1228046bc788c010755122ae35122427fabb6793c90095868106bae9f347","schema_version":"1.0","event_id":"sha256:ac0e1228046bc788c010755122ae35122427fabb6793c90095868106bae9f347"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:IDD5ZJRU2TSOXJU7RJTJVBGHYN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"D-branes and Azumaya/matrix noncommutative differential geometry,II: Azumaya/matrix supermanifolds and differentiable maps therefrom -- with a view toward dynamical fermionic D-branes in string theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.DG","math.SG"],"primary_cat":"hep-th","authors_text":"Chien-Hao Liu, Shing-Tung Yau","submitted_at":"2014-12-02T03:27:30Z","abstract_excerpt":"In this Part II of D(11), we introduce new objects: super-$C^k$-schemes and Azumaya super-$C^k$-manifolds with a fundamental module (or, synonymously, matrix super-$C^k$-manifolds with a fundamental module), and extend the study in D(11.1) ([L-Y3], arXiv:1406.0929 [math.DG]) to define the notion of `differentiable maps from an Azumaya/matrix supermanifold with a fundamental module to a real manifold or supermanifold'. This allows us to introduce the notion of `fermionic D-branes' in two different styles, one parallels Ramond-Neveu-Schwarz fermionic string and the other Green-Schwarz fermionic "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.0771","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":"2026-05-18T02:32:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4FRAMi3HSVZhtrApW/+EkT+M7lr4KKN1/R33/YZppoQGIwLXL2wtxZk7aMDR1D7PFt/6dFvbMzuCShL4lQKQAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T12:08:33.568942Z"},"content_sha256":"8e0f17a17707f38335f305b7b5019c2cc8bd164ccd7935242d1992f189423dc6","schema_version":"1.0","event_id":"sha256:8e0f17a17707f38335f305b7b5019c2cc8bd164ccd7935242d1992f189423dc6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IDD5ZJRU2TSOXJU7RJTJVBGHYN/bundle.json","state_url":"https://pith.science/pith/IDD5ZJRU2TSOXJU7RJTJVBGHYN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IDD5ZJRU2TSOXJU7RJTJVBGHYN/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":"2026-05-30T12:08:33Z","links":{"resolver":"https://pith.science/pith/IDD5ZJRU2TSOXJU7RJTJVBGHYN","bundle":"https://pith.science/pith/IDD5ZJRU2TSOXJU7RJTJVBGHYN/bundle.json","state":"https://pith.science/pith/IDD5ZJRU2TSOXJU7RJTJVBGHYN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IDD5ZJRU2TSOXJU7RJTJVBGHYN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:IDD5ZJRU2TSOXJU7RJTJVBGHYN","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":"5765831f1a1888e901a301bfcc422c5ec5c08432f0be9265d36a5ce4041200c4","cross_cats_sorted":["math.AG","math.DG","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-12-02T03:27:30Z","title_canon_sha256":"a7c1d93d60ebf596f77ad1eea6eaf45260c85ecc32dc08e0cc0ca2869c768de5"},"schema_version":"1.0","source":{"id":"1412.0771","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.0771","created_at":"2026-05-18T02:32:21Z"},{"alias_kind":"arxiv_version","alias_value":"1412.0771v1","created_at":"2026-05-18T02:32:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.0771","created_at":"2026-05-18T02:32:21Z"},{"alias_kind":"pith_short_12","alias_value":"IDD5ZJRU2TSO","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"IDD5ZJRU2TSOXJU7","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"IDD5ZJRU","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:8e0f17a17707f38335f305b7b5019c2cc8bd164ccd7935242d1992f189423dc6","target":"graph","created_at":"2026-05-18T02:32:21Z","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":"In this Part II of D(11), we introduce new objects: super-$C^k$-schemes and Azumaya super-$C^k$-manifolds with a fundamental module (or, synonymously, matrix super-$C^k$-manifolds with a fundamental module), and extend the study in D(11.1) ([L-Y3], arXiv:1406.0929 [math.DG]) to define the notion of `differentiable maps from an Azumaya/matrix supermanifold with a fundamental module to a real manifold or supermanifold'. This allows us to introduce the notion of `fermionic D-branes' in two different styles, one parallels Ramond-Neveu-Schwarz fermionic string and the other Green-Schwarz fermionic ","authors_text":"Chien-Hao Liu, Shing-Tung Yau","cross_cats":["math.AG","math.DG","math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-12-02T03:27:30Z","title":"D-branes and Azumaya/matrix noncommutative differential geometry,II: Azumaya/matrix supermanifolds and differentiable maps therefrom -- with a view toward dynamical fermionic D-branes in string theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.0771","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:ac0e1228046bc788c010755122ae35122427fabb6793c90095868106bae9f347","target":"record","created_at":"2026-05-18T02:32:21Z","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":"5765831f1a1888e901a301bfcc422c5ec5c08432f0be9265d36a5ce4041200c4","cross_cats_sorted":["math.AG","math.DG","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-12-02T03:27:30Z","title_canon_sha256":"a7c1d93d60ebf596f77ad1eea6eaf45260c85ecc32dc08e0cc0ca2869c768de5"},"schema_version":"1.0","source":{"id":"1412.0771","kind":"arxiv","version":1}},"canonical_sha256":"40c7dca634d4e4eba69f8a669a84c7c367a925bbf968daae5de2935c64637a5a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"40c7dca634d4e4eba69f8a669a84c7c367a925bbf968daae5de2935c64637a5a","first_computed_at":"2026-05-18T02:32:21.251782Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:32:21.251782Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HJpxWsUY/kDqUk5Kp+yHozaIM6yIwzZ4TGP65sszGehbvWcSSy6r1qshxEQoESa4wHaiqLBue+C/aRaSi/H8CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:32:21.252163Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.0771","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ac0e1228046bc788c010755122ae35122427fabb6793c90095868106bae9f347","sha256:8e0f17a17707f38335f305b7b5019c2cc8bd164ccd7935242d1992f189423dc6"],"state_sha256":"afe9e746b5ea531faf1d384d8374c54af2d2b8702a656b8db2b79a53446b545f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6sjO9ThSbUpvyDl//Sw5+5+xrc18c2YUnNbiJe2MIRP0QRvvoNu/dC3iMvLtUXKhilkJRlP8SDvLjarLa8QwBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T12:08:33.572671Z","bundle_sha256":"e580f68f1ff543f40f2ca167932c68e92c9bc97d7b185977d339df975fc8ac99"}}