{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:ZGLTZ2FMSX75QINY4JKQ6HNIF6","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":"429c3efb2e2e7113f2f0aae31324185eac96c1608b9f87c64a493d6bb6bb0bfa","cross_cats_sorted":["hep-lat"],"license":"","primary_cat":"hep-th","submitted_at":"2006-09-23T13:53:24Z","title_canon_sha256":"f9c1307d07af1447eb7e0b5cc11eebd571914a334506c6ccfe3c2f2f1ef48b94"},"schema_version":"1.0","source":{"id":"hep-th/0609166","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0609166","created_at":"2026-07-04T15:26:07Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0609166v2","created_at":"2026-07-04T15:26:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0609166","created_at":"2026-07-04T15:26:07Z"},{"alias_kind":"pith_short_12","alias_value":"ZGLTZ2FMSX75","created_at":"2026-07-04T15:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"ZGLTZ2FMSX75QINY","created_at":"2026-07-04T15:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"ZGLTZ2FM","created_at":"2026-07-04T15:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:03cbe2334bf9f98ad310d174b2aee5d39e18966fb5e1b78c7033d22b73527645","target":"graph","created_at":"2026-07-04T15:26:07Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/hep-th/0609166/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We give an argument for deriving analytically the infrared ``Abelian'' dominance in a gauge invariant way for the Wilson loop average in SU(2) Yang--Mills theory. In other words, we propose a possible mechanism for realizing the dynamical Abelian projection in the SU(2) gauge-invariant manner without breaking color symmetry. This supports validity of the dual superconductivity picture for quark confinement. We also discuss the stability of the vacuum with magnetic condensation as a by-product of this result.","authors_text":"Japan), Kei-Ichi Kondo (Chiba Univ.","cross_cats":["hep-lat"],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"2006-09-23T13:53:24Z","title":"Gauge-invariant gluon mass, infrared Abelian dominance and stability of magnetic vacuum"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0609166","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":"sha256:9b214ca68abba860a3c59cf897cbbe47b1e9093e84496d8d3610c492fc685c54","target":"record","created_at":"2026-07-04T15:26:07Z","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":"429c3efb2e2e7113f2f0aae31324185eac96c1608b9f87c64a493d6bb6bb0bfa","cross_cats_sorted":["hep-lat"],"license":"","primary_cat":"hep-th","submitted_at":"2006-09-23T13:53:24Z","title_canon_sha256":"f9c1307d07af1447eb7e0b5cc11eebd571914a334506c6ccfe3c2f2f1ef48b94"},"schema_version":"1.0","source":{"id":"hep-th/0609166","kind":"arxiv","version":2}},"canonical_sha256":"c9973ce8ac95ffd821b8e2550f1da82fa53b30439cb609a7c60f20deb3fc6ad1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c9973ce8ac95ffd821b8e2550f1da82fa53b30439cb609a7c60f20deb3fc6ad1","first_computed_at":"2026-07-04T15:26:07.751101Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:26:07.751101Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f6JwvT+4strvQsCUhopteMJIGlukHJri8jkDi0O7gI8MyzlQuNj5nCSirzNxof6adFhQxZk2rFxW7fZbHGAODg==","signature_status":"signed_v1","signed_at":"2026-07-04T15:26:07.751518Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/0609166","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9b214ca68abba860a3c59cf897cbbe47b1e9093e84496d8d3610c492fc685c54","sha256:03cbe2334bf9f98ad310d174b2aee5d39e18966fb5e1b78c7033d22b73527645"],"state_sha256":"118ba2ad8893e7b31f40b05e760121bd5a9222aa3118746ed3d0183db37c5db6"}