{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:PFSV4WC6ZRG6IISGYD4IALXPYD","short_pith_number":"pith:PFSV4WC6","canonical_record":{"source":{"id":"1501.06904","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2015-01-27T20:56:27Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"757006da4fa8c19f26f4b0f49dd16a67c6d9b8627a8c6bd40f34aea6a709fe58","abstract_canon_sha256":"69579fbcd42f58ecee5c647e02fcaa7cacc56a949635fe415d4a2d788af24830"},"schema_version":"1.0"},"canonical_sha256":"79655e585ecc4de42246c0f8802eefc0cd4054ee1bf68e7a5659ebd2abd7c3fe","source":{"kind":"arxiv","id":"1501.06904","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.06904","created_at":"2026-05-18T02:27:58Z"},{"alias_kind":"arxiv_version","alias_value":"1501.06904v2","created_at":"2026-05-18T02:27:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.06904","created_at":"2026-05-18T02:27:58Z"},{"alias_kind":"pith_short_12","alias_value":"PFSV4WC6ZRG6","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PFSV4WC6ZRG6IISG","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PFSV4WC6","created_at":"2026-05-18T12:29:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:PFSV4WC6ZRG6IISGYD4IALXPYD","target":"record","payload":{"canonical_record":{"source":{"id":"1501.06904","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2015-01-27T20:56:27Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"757006da4fa8c19f26f4b0f49dd16a67c6d9b8627a8c6bd40f34aea6a709fe58","abstract_canon_sha256":"69579fbcd42f58ecee5c647e02fcaa7cacc56a949635fe415d4a2d788af24830"},"schema_version":"1.0"},"canonical_sha256":"79655e585ecc4de42246c0f8802eefc0cd4054ee1bf68e7a5659ebd2abd7c3fe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:58.248136Z","signature_b64":"JGVQ/jUudh517W66TS66Q7usztk2OtFDpTlZxER1PJjZ1CWff8aAnKQUylSDDt7Q73v6xtsauQi3SMghBgiqBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"79655e585ecc4de42246c0f8802eefc0cd4054ee1bf68e7a5659ebd2abd7c3fe","last_reissued_at":"2026-05-18T02:27:58.247595Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:58.247595Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.06904","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:27:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2c4m7oLRSe9fO0rWBzT9ES5nZRDwpVE+39+FzO6aAHeOg3uuM/czHKUX+xE+ojOJbSkB1bssd8QPIjFnIWo/Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T10:43:46.598651Z"},"content_sha256":"eae238c1dc30816ee36fbd75e2d37740dd692e3def1fc3d2d4d3db65b03f6fe3","schema_version":"1.0","event_id":"sha256:eae238c1dc30816ee36fbd75e2d37740dd692e3def1fc3d2d4d3db65b03f6fe3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:PFSV4WC6ZRG6IISGYD4IALXPYD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Correlation functions of Polyakov loops at tree level","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"hep-ph","authors_text":"Robert D. Pisarski, Vladimir V. Skokov","submitted_at":"2015-01-27T20:56:27Z","abstract_excerpt":"We compute the correlation functions of Polyakov loops in $SU(N_c)$ gauge theories by explicitly summing all diagrams at tree level in two special cases, for $N_c = 2$ and $N_c = \\infty$. When $N_c =2$ we find the expected we find Coulomb-like behavior at short distances, $\\sim 1/x$ as the distance $x \\rightarrow 0$. In the planar limit at $N_c = \\infty$ we find a weaker singularity, $\\sim 1/\\sqrt{x}$ as $x \\rightarrow 0$. In each case, at short distances the behavior of the correlation functions between two Polyakov loops, and the corresponding Wilson loop, are the same. We suggest that such "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06904","kind":"arxiv","version":2},"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":"2026-05-18T02:27:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ceSqYwWI5NCoOrXCmhLKCmOIfkbSMiGJnSGFgPMqVFZQTLzNHl6bRwdX9/GiyBs8Ch0Fsn+eKgcSt3gHLDiEDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T10:43:46.598992Z"},"content_sha256":"dbac6fd7690b5f6a52846fc428a854ede828585dad6f23238bbac44585eb8388","schema_version":"1.0","event_id":"sha256:dbac6fd7690b5f6a52846fc428a854ede828585dad6f23238bbac44585eb8388"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PFSV4WC6ZRG6IISGYD4IALXPYD/bundle.json","state_url":"https://pith.science/pith/PFSV4WC6ZRG6IISGYD4IALXPYD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PFSV4WC6ZRG6IISGYD4IALXPYD/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":"2026-05-28T10:43:46Z","links":{"resolver":"https://pith.science/pith/PFSV4WC6ZRG6IISGYD4IALXPYD","bundle":"https://pith.science/pith/PFSV4WC6ZRG6IISGYD4IALXPYD/bundle.json","state":"https://pith.science/pith/PFSV4WC6ZRG6IISGYD4IALXPYD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PFSV4WC6ZRG6IISGYD4IALXPYD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:PFSV4WC6ZRG6IISGYD4IALXPYD","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":"69579fbcd42f58ecee5c647e02fcaa7cacc56a949635fe415d4a2d788af24830","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2015-01-27T20:56:27Z","title_canon_sha256":"757006da4fa8c19f26f4b0f49dd16a67c6d9b8627a8c6bd40f34aea6a709fe58"},"schema_version":"1.0","source":{"id":"1501.06904","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.06904","created_at":"2026-05-18T02:27:58Z"},{"alias_kind":"arxiv_version","alias_value":"1501.06904v2","created_at":"2026-05-18T02:27:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.06904","created_at":"2026-05-18T02:27:58Z"},{"alias_kind":"pith_short_12","alias_value":"PFSV4WC6ZRG6","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PFSV4WC6ZRG6IISG","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PFSV4WC6","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:dbac6fd7690b5f6a52846fc428a854ede828585dad6f23238bbac44585eb8388","target":"graph","created_at":"2026-05-18T02:27:58Z","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":"We compute the correlation functions of Polyakov loops in $SU(N_c)$ gauge theories by explicitly summing all diagrams at tree level in two special cases, for $N_c = 2$ and $N_c = \\infty$. When $N_c =2$ we find the expected we find Coulomb-like behavior at short distances, $\\sim 1/x$ as the distance $x \\rightarrow 0$. In the planar limit at $N_c = \\infty$ we find a weaker singularity, $\\sim 1/\\sqrt{x}$ as $x \\rightarrow 0$. In each case, at short distances the behavior of the correlation functions between two Polyakov loops, and the corresponding Wilson loop, are the same. We suggest that such ","authors_text":"Robert D. Pisarski, Vladimir V. Skokov","cross_cats":["hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2015-01-27T20:56:27Z","title":"Correlation functions of Polyakov loops at tree level"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06904","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:eae238c1dc30816ee36fbd75e2d37740dd692e3def1fc3d2d4d3db65b03f6fe3","target":"record","created_at":"2026-05-18T02:27:58Z","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":"69579fbcd42f58ecee5c647e02fcaa7cacc56a949635fe415d4a2d788af24830","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2015-01-27T20:56:27Z","title_canon_sha256":"757006da4fa8c19f26f4b0f49dd16a67c6d9b8627a8c6bd40f34aea6a709fe58"},"schema_version":"1.0","source":{"id":"1501.06904","kind":"arxiv","version":2}},"canonical_sha256":"79655e585ecc4de42246c0f8802eefc0cd4054ee1bf68e7a5659ebd2abd7c3fe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"79655e585ecc4de42246c0f8802eefc0cd4054ee1bf68e7a5659ebd2abd7c3fe","first_computed_at":"2026-05-18T02:27:58.247595Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:58.247595Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JGVQ/jUudh517W66TS66Q7usztk2OtFDpTlZxER1PJjZ1CWff8aAnKQUylSDDt7Q73v6xtsauQi3SMghBgiqBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:58.248136Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.06904","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eae238c1dc30816ee36fbd75e2d37740dd692e3def1fc3d2d4d3db65b03f6fe3","sha256:dbac6fd7690b5f6a52846fc428a854ede828585dad6f23238bbac44585eb8388"],"state_sha256":"6ab3982f89e25dd57e2f63332a86927f63c11798957a95633228766fa63747d1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pylEN1JvANzw/N/JQo0f8Y3cqM8JOaf3V+Mng69kYBT3plbV3Q2S8DqseaBbqXS3cuHIZtN5YnksarxEJcLvCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T10:43:46.601078Z","bundle_sha256":"a8df88d3059928fab147725f846b08cda5778b846657888e1ed633cb0057ac06"}}