{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:VUJ6C7YJCFOOKJHI7HKP6HPKMY","short_pith_number":"pith:VUJ6C7YJ","canonical_record":{"source":{"id":"1907.00155","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-06-29T06:47:10Z","cross_cats_sorted":["hep-th","math.DG","math.MP"],"title_canon_sha256":"a7357905cf4c2faeeef74713a54cea23bef3a4bfc455eefb041e095d63163b08","abstract_canon_sha256":"d443c899cb82ca834fe44c9f97bab9cd108d532595778c6818bbdbdcfc76bfd0"},"schema_version":"1.0"},"canonical_sha256":"ad13e17f09115ce524e8f9d4ff1dea6616c6a8bec111c712909935df2c0a28ef","source":{"kind":"arxiv","id":"1907.00155","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.00155","created_at":"2026-05-17T23:41:57Z"},{"alias_kind":"arxiv_version","alias_value":"1907.00155v1","created_at":"2026-05-17T23:41:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.00155","created_at":"2026-05-17T23:41:57Z"},{"alias_kind":"pith_short_12","alias_value":"VUJ6C7YJCFOO","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"VUJ6C7YJCFOOKJHI","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"VUJ6C7YJ","created_at":"2026-05-18T12:33:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:VUJ6C7YJCFOOKJHI7HKP6HPKMY","target":"record","payload":{"canonical_record":{"source":{"id":"1907.00155","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-06-29T06:47:10Z","cross_cats_sorted":["hep-th","math.DG","math.MP"],"title_canon_sha256":"a7357905cf4c2faeeef74713a54cea23bef3a4bfc455eefb041e095d63163b08","abstract_canon_sha256":"d443c899cb82ca834fe44c9f97bab9cd108d532595778c6818bbdbdcfc76bfd0"},"schema_version":"1.0"},"canonical_sha256":"ad13e17f09115ce524e8f9d4ff1dea6616c6a8bec111c712909935df2c0a28ef","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:57.304281Z","signature_b64":"QQqr7F64pgTfOTo5b62Y+Dl8pjlJb8WHEYjimbAmRL397qZNPna1cOE9pcH5F2bzzSFZDgL1+5qAyTW6ixOIDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ad13e17f09115ce524e8f9d4ff1dea6616c6a8bec111c712909935df2c0a28ef","last_reissued_at":"2026-05-17T23:41:57.303594Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:57.303594Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1907.00155","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":"2026-05-17T23:41:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1VwdDyvFHj1GYcCOnFBWZT7Ew3BvDzLNSJXEpu7/KG/3nutgDyNXslkLV72RaOT05qaOVs3RhT/pDpqX2LkIAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T04:40:56.567873Z"},"content_sha256":"6547834b57de31be896778fec7f3ba0750ecacb914c76a686b1cf65b0a07bf61","schema_version":"1.0","event_id":"sha256:6547834b57de31be896778fec7f3ba0750ecacb914c76a686b1cf65b0a07bf61"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:VUJ6C7YJCFOOKJHI7HKP6HPKMY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Operational total space theory of principal 2-bundles II: 2-connections and 1- and 2--gauge transformations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.DG","math.MP"],"primary_cat":"math-ph","authors_text":"Roberto Zucchini","submitted_at":"2019-06-29T06:47:10Z","abstract_excerpt":"The geometry of the total space of a principal bundle with regard to the action of the bundle's structure group is elegantly described by the bundle's operation, a collection of derivations consisting of the de Rham differential and the contraction and Lie derivatives of all vertical vector fields and satisfying the six Cartan relations. Connections and gauge transformations are defined by the way they behave under the action of the operation's derivations. In the first paper of a series of two extending the ordinary theory, we constructed an operational total space theory of strict principal "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.00155","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":"2026-05-17T23:41:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HUPKjVPLuJzdGWYaFUrHN5nffEp5LR5V0EEEZPub3TaLSHSdcogKWkYLtS0csKq4ZU5laQ5Vq+VtXZDgWoKvCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T04:40:56.568593Z"},"content_sha256":"93fb2379b25876c0d5f24e594bd8b8d3535b9f9d20cbe382985d4cf1b340f9e1","schema_version":"1.0","event_id":"sha256:93fb2379b25876c0d5f24e594bd8b8d3535b9f9d20cbe382985d4cf1b340f9e1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VUJ6C7YJCFOOKJHI7HKP6HPKMY/bundle.json","state_url":"https://pith.science/pith/VUJ6C7YJCFOOKJHI7HKP6HPKMY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VUJ6C7YJCFOOKJHI7HKP6HPKMY/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":"2026-05-26T04:40:56Z","links":{"resolver":"https://pith.science/pith/VUJ6C7YJCFOOKJHI7HKP6HPKMY","bundle":"https://pith.science/pith/VUJ6C7YJCFOOKJHI7HKP6HPKMY/bundle.json","state":"https://pith.science/pith/VUJ6C7YJCFOOKJHI7HKP6HPKMY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VUJ6C7YJCFOOKJHI7HKP6HPKMY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:VUJ6C7YJCFOOKJHI7HKP6HPKMY","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":"d443c899cb82ca834fe44c9f97bab9cd108d532595778c6818bbdbdcfc76bfd0","cross_cats_sorted":["hep-th","math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-06-29T06:47:10Z","title_canon_sha256":"a7357905cf4c2faeeef74713a54cea23bef3a4bfc455eefb041e095d63163b08"},"schema_version":"1.0","source":{"id":"1907.00155","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.00155","created_at":"2026-05-17T23:41:57Z"},{"alias_kind":"arxiv_version","alias_value":"1907.00155v1","created_at":"2026-05-17T23:41:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.00155","created_at":"2026-05-17T23:41:57Z"},{"alias_kind":"pith_short_12","alias_value":"VUJ6C7YJCFOO","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"VUJ6C7YJCFOOKJHI","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"VUJ6C7YJ","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:93fb2379b25876c0d5f24e594bd8b8d3535b9f9d20cbe382985d4cf1b340f9e1","target":"graph","created_at":"2026-05-17T23:41:57Z","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":"The geometry of the total space of a principal bundle with regard to the action of the bundle's structure group is elegantly described by the bundle's operation, a collection of derivations consisting of the de Rham differential and the contraction and Lie derivatives of all vertical vector fields and satisfying the six Cartan relations. Connections and gauge transformations are defined by the way they behave under the action of the operation's derivations. In the first paper of a series of two extending the ordinary theory, we constructed an operational total space theory of strict principal ","authors_text":"Roberto Zucchini","cross_cats":["hep-th","math.DG","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-06-29T06:47:10Z","title":"Operational total space theory of principal 2-bundles II: 2-connections and 1- and 2--gauge transformations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.00155","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":"sha256:6547834b57de31be896778fec7f3ba0750ecacb914c76a686b1cf65b0a07bf61","target":"record","created_at":"2026-05-17T23:41:57Z","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":"d443c899cb82ca834fe44c9f97bab9cd108d532595778c6818bbdbdcfc76bfd0","cross_cats_sorted":["hep-th","math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-06-29T06:47:10Z","title_canon_sha256":"a7357905cf4c2faeeef74713a54cea23bef3a4bfc455eefb041e095d63163b08"},"schema_version":"1.0","source":{"id":"1907.00155","kind":"arxiv","version":1}},"canonical_sha256":"ad13e17f09115ce524e8f9d4ff1dea6616c6a8bec111c712909935df2c0a28ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ad13e17f09115ce524e8f9d4ff1dea6616c6a8bec111c712909935df2c0a28ef","first_computed_at":"2026-05-17T23:41:57.303594Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:57.303594Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QQqr7F64pgTfOTo5b62Y+Dl8pjlJb8WHEYjimbAmRL397qZNPna1cOE9pcH5F2bzzSFZDgL1+5qAyTW6ixOIDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:57.304281Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.00155","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6547834b57de31be896778fec7f3ba0750ecacb914c76a686b1cf65b0a07bf61","sha256:93fb2379b25876c0d5f24e594bd8b8d3535b9f9d20cbe382985d4cf1b340f9e1"],"state_sha256":"a78193fc27c329a3c4623a36c4ec5d077a4a0ab5b83324930c3f9eef130852b2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mzguXMb3T+4j0Cfl2qehbB2CMPR/FwHJsMdD+gAoELbjde42Rfqr5l6SWpsZ48XB9CLbT3LX79roOTu/H4RXAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T04:40:56.574254Z","bundle_sha256":"b71b88ea26bc70b85a181d3acfa3027b8ee677217e98883fc6c7be5c13bd1077"}}