{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:E5ZKN7ELIWXAKRPVZ7YP4K7GHK","short_pith_number":"pith:E5ZKN7EL","canonical_record":{"source":{"id":"2606.05978","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2026-06-04T10:19:23Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"03e00f83c50f40497dbd0e6b78cc4655ca0ba4aba77fcdf620abae8ee984e0c5","abstract_canon_sha256":"1bb145672cfbd4f34f425f3855978e1eb4a7844f0b86ccb3de635cbbd3b0e889"},"schema_version":"1.0"},"canonical_sha256":"2772a6fc8b45ae0545f5cff0fe2be63a87fa6a5efe09a7b73413eb1e99126fb3","source":{"kind":"arxiv","id":"2606.05978","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.05978","created_at":"2026-06-05T01:15:29Z"},{"alias_kind":"arxiv_version","alias_value":"2606.05978v1","created_at":"2026-06-05T01:15:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.05978","created_at":"2026-06-05T01:15:29Z"},{"alias_kind":"pith_short_12","alias_value":"E5ZKN7ELIWXA","created_at":"2026-06-05T01:15:29Z"},{"alias_kind":"pith_short_16","alias_value":"E5ZKN7ELIWXAKRPV","created_at":"2026-06-05T01:15:29Z"},{"alias_kind":"pith_short_8","alias_value":"E5ZKN7EL","created_at":"2026-06-05T01:15:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:E5ZKN7ELIWXAKRPVZ7YP4K7GHK","target":"record","payload":{"canonical_record":{"source":{"id":"2606.05978","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2026-06-04T10:19:23Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"03e00f83c50f40497dbd0e6b78cc4655ca0ba4aba77fcdf620abae8ee984e0c5","abstract_canon_sha256":"1bb145672cfbd4f34f425f3855978e1eb4a7844f0b86ccb3de635cbbd3b0e889"},"schema_version":"1.0"},"canonical_sha256":"2772a6fc8b45ae0545f5cff0fe2be63a87fa6a5efe09a7b73413eb1e99126fb3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-05T01:15:29.276666Z","signature_b64":"7spX7GkfBd+D+qqJHh0YJF0hE0PDk1WUrMvfRjuW7SxtZj4Xf1sG/R1UscNupq4MALi3UjeQt3NWOZvOb2cFDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2772a6fc8b45ae0545f5cff0fe2be63a87fa6a5efe09a7b73413eb1e99126fb3","last_reissued_at":"2026-06-05T01:15:29.276265Z","signature_status":"signed_v1","first_computed_at":"2026-06-05T01:15:29.276265Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.05978","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":"2026-06-05T01:15:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g7Vp3KhQxDUvRfS0j0vqN00vsvUsRJSWcAW5rI7XqX4IAb4KVh0mqmRkH7w8TqzhtNKqi2b4Ifc4Mz9bX+v9Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T07:48:55.675401Z"},"content_sha256":"5fc1aea60511fcbb35800d448370c1980d92a62f8e693bd1e037e10d5898bfae","schema_version":"1.0","event_id":"sha256:5fc1aea60511fcbb35800d448370c1980d92a62f8e693bd1e037e10d5898bfae"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:E5ZKN7ELIWXAKRPVZ7YP4K7GHK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lecture notes: Introduction to the Off-shell Double Copy Program","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"hep-th","authors_text":"Eric Lescano","submitted_at":"2026-06-04T10:19:23Z","abstract_excerpt":"The present notes are based on a series of lectures prepared for an introductory eight-class course on the modern framework of the off-shell double copy. The course was held from April 16 to May 4, 2026, at Universidad de Buenos Aires (UBA). These lectures, aimed at PhD and master's students, are self-contained and require only a basic knowledge of classical field theory. The main goal is to review the fundamental concepts of gauge and gravitational theories in order to explore the off-shell frameworks of the single and double copy. In the final part of the course, we explore modern approaches"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.05978","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.05978/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":"2026-06-05T01:15:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OYO3zRGziXrd4M/2qdhIDkWg/b0gODyzzwF9c68N5A0GeybxCeg7UMEKNerJ246g80gID/pQNucsM5psAlIrDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T07:48:55.675775Z"},"content_sha256":"a419cfcfddc89caa77da06284c10b721a6b09545961439aa22b146c096a37aeb","schema_version":"1.0","event_id":"sha256:a419cfcfddc89caa77da06284c10b721a6b09545961439aa22b146c096a37aeb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E5ZKN7ELIWXAKRPVZ7YP4K7GHK/bundle.json","state_url":"https://pith.science/pith/E5ZKN7ELIWXAKRPVZ7YP4K7GHK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E5ZKN7ELIWXAKRPVZ7YP4K7GHK/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":"2026-06-28T07:48:55Z","links":{"resolver":"https://pith.science/pith/E5ZKN7ELIWXAKRPVZ7YP4K7GHK","bundle":"https://pith.science/pith/E5ZKN7ELIWXAKRPVZ7YP4K7GHK/bundle.json","state":"https://pith.science/pith/E5ZKN7ELIWXAKRPVZ7YP4K7GHK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E5ZKN7ELIWXAKRPVZ7YP4K7GHK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:E5ZKN7ELIWXAKRPVZ7YP4K7GHK","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":"1bb145672cfbd4f34f425f3855978e1eb4a7844f0b86ccb3de635cbbd3b0e889","cross_cats_sorted":["gr-qc"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2026-06-04T10:19:23Z","title_canon_sha256":"03e00f83c50f40497dbd0e6b78cc4655ca0ba4aba77fcdf620abae8ee984e0c5"},"schema_version":"1.0","source":{"id":"2606.05978","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.05978","created_at":"2026-06-05T01:15:29Z"},{"alias_kind":"arxiv_version","alias_value":"2606.05978v1","created_at":"2026-06-05T01:15:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.05978","created_at":"2026-06-05T01:15:29Z"},{"alias_kind":"pith_short_12","alias_value":"E5ZKN7ELIWXA","created_at":"2026-06-05T01:15:29Z"},{"alias_kind":"pith_short_16","alias_value":"E5ZKN7ELIWXAKRPV","created_at":"2026-06-05T01:15:29Z"},{"alias_kind":"pith_short_8","alias_value":"E5ZKN7EL","created_at":"2026-06-05T01:15:29Z"}],"graph_snapshots":[{"event_id":"sha256:a419cfcfddc89caa77da06284c10b721a6b09545961439aa22b146c096a37aeb","target":"graph","created_at":"2026-06-05T01:15:29Z","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/2606.05978/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The present notes are based on a series of lectures prepared for an introductory eight-class course on the modern framework of the off-shell double copy. The course was held from April 16 to May 4, 2026, at Universidad de Buenos Aires (UBA). These lectures, aimed at PhD and master's students, are self-contained and require only a basic knowledge of classical field theory. The main goal is to review the fundamental concepts of gauge and gravitational theories in order to explore the off-shell frameworks of the single and double copy. In the final part of the course, we explore modern approaches","authors_text":"Eric Lescano","cross_cats":["gr-qc"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2026-06-04T10:19:23Z","title":"Lecture notes: Introduction to the Off-shell Double Copy Program"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.05978","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":"sha256:5fc1aea60511fcbb35800d448370c1980d92a62f8e693bd1e037e10d5898bfae","target":"record","created_at":"2026-06-05T01:15:29Z","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":"1bb145672cfbd4f34f425f3855978e1eb4a7844f0b86ccb3de635cbbd3b0e889","cross_cats_sorted":["gr-qc"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2026-06-04T10:19:23Z","title_canon_sha256":"03e00f83c50f40497dbd0e6b78cc4655ca0ba4aba77fcdf620abae8ee984e0c5"},"schema_version":"1.0","source":{"id":"2606.05978","kind":"arxiv","version":1}},"canonical_sha256":"2772a6fc8b45ae0545f5cff0fe2be63a87fa6a5efe09a7b73413eb1e99126fb3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2772a6fc8b45ae0545f5cff0fe2be63a87fa6a5efe09a7b73413eb1e99126fb3","first_computed_at":"2026-06-05T01:15:29.276265Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-05T01:15:29.276265Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7spX7GkfBd+D+qqJHh0YJF0hE0PDk1WUrMvfRjuW7SxtZj4Xf1sG/R1UscNupq4MALi3UjeQt3NWOZvOb2cFDw==","signature_status":"signed_v1","signed_at":"2026-06-05T01:15:29.276666Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.05978","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5fc1aea60511fcbb35800d448370c1980d92a62f8e693bd1e037e10d5898bfae","sha256:a419cfcfddc89caa77da06284c10b721a6b09545961439aa22b146c096a37aeb"],"state_sha256":"c83c6c1716c9ee8c8d7017d72cf1b7e69482a46d6ebb91f5b5f30287ad77e405"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OfKwp2ePxOE6zYonzFQpX1X50P0bHwZgh8fEZ7PXAD7EJWwCpy7X+W03MTcYAytCBCxlVrYK3QRbdPxKeS+aAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T07:48:55.677816Z","bundle_sha256":"b97f2497235bda92487501f0b2a55fb0fd1a56704a01d33989f4dc3aa4f590cb"}}