{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:RIQJOB3XWFU5AVURBGPTAK66X7","short_pith_number":"pith:RIQJOB3X","canonical_record":{"source":{"id":"1106.0639","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-06-03T13:43:01Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"1e7119a95aa2275d96bc48f6f08bfca5d7ecd85b040febf3d15e705faadd87d6","abstract_canon_sha256":"a75bb4752c3fa99106fd989933d9de28edd9859945d8179c4d8c8ae28573930f"},"schema_version":"1.0"},"canonical_sha256":"8a20970777b169d05691099f302bdebfd66914ab448968b50ffffde75ce5765c","source":{"kind":"arxiv","id":"1106.0639","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.0639","created_at":"2026-05-18T04:14:07Z"},{"alias_kind":"arxiv_version","alias_value":"1106.0639v4","created_at":"2026-05-18T04:14:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.0639","created_at":"2026-05-18T04:14:07Z"},{"alias_kind":"pith_short_12","alias_value":"RIQJOB3XWFU5","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"RIQJOB3XWFU5AVUR","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"RIQJOB3X","created_at":"2026-05-18T12:26:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:RIQJOB3XWFU5AVURBGPTAK66X7","target":"record","payload":{"canonical_record":{"source":{"id":"1106.0639","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-06-03T13:43:01Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"1e7119a95aa2275d96bc48f6f08bfca5d7ecd85b040febf3d15e705faadd87d6","abstract_canon_sha256":"a75bb4752c3fa99106fd989933d9de28edd9859945d8179c4d8c8ae28573930f"},"schema_version":"1.0"},"canonical_sha256":"8a20970777b169d05691099f302bdebfd66914ab448968b50ffffde75ce5765c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:14:07.565849Z","signature_b64":"SwBHloTU0Jl/bmtyO71+b3Puj9+T0zScBosKeh6n/5BYnZysDW8GpBs1p2G76ZG0eYsR9ZfRYqYGG8iKFsDhAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8a20970777b169d05691099f302bdebfd66914ab448968b50ffffde75ce5765c","last_reissued_at":"2026-05-18T04:14:07.565335Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:14:07.565335Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1106.0639","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:14:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RmihS2GBBPrLOykAmVBtIIXSrQbu1gFHhN01Xl2EHggpXzDqE1a3ge8i7TvR2QDPG0AhRP/u/B6WtUETUO+uCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T02:19:36.385233Z"},"content_sha256":"94df1ae04b2c8e2a64ca9d9102edefa7384c8231af7a7fcdeaf0de6d022f396b","schema_version":"1.0","event_id":"sha256:94df1ae04b2c8e2a64ca9d9102edefa7384c8231af7a7fcdeaf0de6d022f396b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:RIQJOB3XWFU5AVURBGPTAK66X7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Classical Noncommutative Electrodynamics with External Source","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"hep-th","authors_text":"A. E. Shabad, D. M. Gitman, D. V. Vassilevich, T. C. Adorno","submitted_at":"2011-06-03T13:43:01Z","abstract_excerpt":"In a $U(1)_{\\star}$-noncommutative (NC) gauge field theory we extend the Seiberg-Witten (SW) map to include the (gauge-invariance-violating) external current and formulate - to the first order in the NC parameter - gauge-covariant classical field equations. We find solutions to these equations in the vacuum and in an external magnetic field, when the 4-current is a static electric charge of a finite size $a$, restricted from below by the elementary length. We impose extra boundary conditions, which we use to rule out all singularities, $1/r$ included, from the solutions. The static charge prov"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.0639","kind":"arxiv","version":4},"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":"2026-05-18T04:14:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MjddpvZwmQ64lgbvdqy/ZLuh2kF4DadY+C42YeHPcGuj4J7cZaKRuSEbv3crvfkyf8Oeu5hg1XhLJzG8tgKcAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T02:19:36.385957Z"},"content_sha256":"ed914fcec8127ec3db278d551cad4734703027c68a90224f3fa3494f78febd62","schema_version":"1.0","event_id":"sha256:ed914fcec8127ec3db278d551cad4734703027c68a90224f3fa3494f78febd62"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RIQJOB3XWFU5AVURBGPTAK66X7/bundle.json","state_url":"https://pith.science/pith/RIQJOB3XWFU5AVURBGPTAK66X7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RIQJOB3XWFU5AVURBGPTAK66X7/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":"2026-05-19T02:19:36Z","links":{"resolver":"https://pith.science/pith/RIQJOB3XWFU5AVURBGPTAK66X7","bundle":"https://pith.science/pith/RIQJOB3XWFU5AVURBGPTAK66X7/bundle.json","state":"https://pith.science/pith/RIQJOB3XWFU5AVURBGPTAK66X7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RIQJOB3XWFU5AVURBGPTAK66X7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:RIQJOB3XWFU5AVURBGPTAK66X7","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":"a75bb4752c3fa99106fd989933d9de28edd9859945d8179c4d8c8ae28573930f","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-06-03T13:43:01Z","title_canon_sha256":"1e7119a95aa2275d96bc48f6f08bfca5d7ecd85b040febf3d15e705faadd87d6"},"schema_version":"1.0","source":{"id":"1106.0639","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.0639","created_at":"2026-05-18T04:14:07Z"},{"alias_kind":"arxiv_version","alias_value":"1106.0639v4","created_at":"2026-05-18T04:14:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.0639","created_at":"2026-05-18T04:14:07Z"},{"alias_kind":"pith_short_12","alias_value":"RIQJOB3XWFU5","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"RIQJOB3XWFU5AVUR","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"RIQJOB3X","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:ed914fcec8127ec3db278d551cad4734703027c68a90224f3fa3494f78febd62","target":"graph","created_at":"2026-05-18T04:14:07Z","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 a $U(1)_{\\star}$-noncommutative (NC) gauge field theory we extend the Seiberg-Witten (SW) map to include the (gauge-invariance-violating) external current and formulate - to the first order in the NC parameter - gauge-covariant classical field equations. We find solutions to these equations in the vacuum and in an external magnetic field, when the 4-current is a static electric charge of a finite size $a$, restricted from below by the elementary length. We impose extra boundary conditions, which we use to rule out all singularities, $1/r$ included, from the solutions. The static charge prov","authors_text":"A. E. Shabad, D. M. Gitman, D. V. Vassilevich, T. C. Adorno","cross_cats":["quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-06-03T13:43:01Z","title":"Classical Noncommutative Electrodynamics with External Source"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.0639","kind":"arxiv","version":4},"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":"sha256:94df1ae04b2c8e2a64ca9d9102edefa7384c8231af7a7fcdeaf0de6d022f396b","target":"record","created_at":"2026-05-18T04:14:07Z","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":"a75bb4752c3fa99106fd989933d9de28edd9859945d8179c4d8c8ae28573930f","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-06-03T13:43:01Z","title_canon_sha256":"1e7119a95aa2275d96bc48f6f08bfca5d7ecd85b040febf3d15e705faadd87d6"},"schema_version":"1.0","source":{"id":"1106.0639","kind":"arxiv","version":4}},"canonical_sha256":"8a20970777b169d05691099f302bdebfd66914ab448968b50ffffde75ce5765c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8a20970777b169d05691099f302bdebfd66914ab448968b50ffffde75ce5765c","first_computed_at":"2026-05-18T04:14:07.565335Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:14:07.565335Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SwBHloTU0Jl/bmtyO71+b3Puj9+T0zScBosKeh6n/5BYnZysDW8GpBs1p2G76ZG0eYsR9ZfRYqYGG8iKFsDhAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:14:07.565849Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.0639","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:94df1ae04b2c8e2a64ca9d9102edefa7384c8231af7a7fcdeaf0de6d022f396b","sha256:ed914fcec8127ec3db278d551cad4734703027c68a90224f3fa3494f78febd62"],"state_sha256":"719dc1fea2925982f43de7b41924046a02e702268109fb4d3cfe18141894b69a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+VLx3e7//8QexjhcfprxyjIaLIXlc6A3YI7rMaZF78FNV0RUcLiUjFzulBpQnFBsadS8Dcg9IBaejSDWnjetCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-19T02:19:36.390233Z","bundle_sha256":"2162bde083b15923875d48d031dbc30a07774ddad715d3616ec772d18b25dd7d"}}