{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:KD522DRZU2UGNKATMMTV6GNKUL","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":"f8d981aae739c24e67a7c96db381563cf1ec3aa65aedb948f191cfaeb2704fbf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-12-17T19:13:44Z","title_canon_sha256":"f615e0b7df58930496a65456a6965ec60f52ce495a1bda499c6f50aec98cf8e3"},"schema_version":"1.0","source":{"id":"1512.05725","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.05725","created_at":"2026-05-18T01:14:01Z"},{"alias_kind":"arxiv_version","alias_value":"1512.05725v2","created_at":"2026-05-18T01:14:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.05725","created_at":"2026-05-18T01:14:01Z"},{"alias_kind":"pith_short_12","alias_value":"KD522DRZU2UG","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"KD522DRZU2UGNKAT","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"KD522DRZ","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:e28bd311b1e2805a42dd77986d0fe293a97c50df924d90d33979dcf731557871","target":"graph","created_at":"2026-05-18T01:14:01Z","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 article we present exact calculations that substantiate a clear picture relating the confining force of QCD to the zero-modes of the Faddeev-Popov (FP) operator $\\mathcal{M}(A) = - \\partial \\cdot D(A)$. This is done in two steps. First we calculate the spectral decomposition of the FP operator and show that the ghost propagator $\\mathcal{G}(k; A) = \\langle \\vec{k}| \\mathcal{M}^{-1}(A) | \\vec{k} \\rangle$ in an external gauge potential $A$ is enhanced at low $k$ in Fourier space for configurations $A$ on the Gribov horizon. This results from the new formula in the low-$k$ regime $\\mathca","authors_text":"Daniel Zwanziger, Patrick Cooper","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-12-17T19:13:44Z","title":"Origin of Confining Force"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.05725","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":"sha256:7f76b6e79de29b5b248ade8d8a635a18a694c294ee85f40b55f61305a29e2090","target":"record","created_at":"2026-05-18T01:14:01Z","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":"f8d981aae739c24e67a7c96db381563cf1ec3aa65aedb948f191cfaeb2704fbf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-12-17T19:13:44Z","title_canon_sha256":"f615e0b7df58930496a65456a6965ec60f52ce495a1bda499c6f50aec98cf8e3"},"schema_version":"1.0","source":{"id":"1512.05725","kind":"arxiv","version":2}},"canonical_sha256":"50fbad0e39a6a866a81363275f19aaa2d6640f8725dc7ca9446672613dfc2697","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"50fbad0e39a6a866a81363275f19aaa2d6640f8725dc7ca9446672613dfc2697","first_computed_at":"2026-05-18T01:14:01.549494Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:14:01.549494Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RUCMN+sDNbqDeWCPyfOktwpVT9Z27P4KXDAQ/6kzWz2Vif4gVIVlXweuw2AkFWCep9/GbgKs6CSznJaZKKwFDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:14:01.550070Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.05725","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7f76b6e79de29b5b248ade8d8a635a18a694c294ee85f40b55f61305a29e2090","sha256:e28bd311b1e2805a42dd77986d0fe293a97c50df924d90d33979dcf731557871"],"state_sha256":"fe81f775f153847d4dc6fb416f4d68b69fd1a7dae84e0befa5409056be4126a6"}