{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:GUR3IHM5XRIE6TLY25YJLWICAX","short_pith_number":"pith:GUR3IHM5","canonical_record":{"source":{"id":"1807.02945","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-07-09T05:12:06Z","cross_cats_sorted":["hep-th","math.CV","math.MP"],"title_canon_sha256":"78260256a26a26fe9b1aa6c24b582bc57a41dbdbd04964be7ef5c108c0cff992","abstract_canon_sha256":"8ff1a908b14f6b40318f10da03f593255d6782c09b6be4868505af715a76b724"},"schema_version":"1.0"},"canonical_sha256":"3523b41d9dbc504f4d78d77095d90205dbe362b570cac934017b607a2d02a0ac","source":{"kind":"arxiv","id":"1807.02945","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.02945","created_at":"2026-07-05T00:30:51Z"},{"alias_kind":"arxiv_version","alias_value":"1807.02945v2","created_at":"2026-07-05T00:30:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.02945","created_at":"2026-07-05T00:30:51Z"},{"alias_kind":"pith_short_12","alias_value":"GUR3IHM5XRIE","created_at":"2026-07-05T00:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"GUR3IHM5XRIE6TLY","created_at":"2026-07-05T00:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"GUR3IHM5","created_at":"2026-07-05T00:30:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:GUR3IHM5XRIE6TLY25YJLWICAX","target":"record","payload":{"canonical_record":{"source":{"id":"1807.02945","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-07-09T05:12:06Z","cross_cats_sorted":["hep-th","math.CV","math.MP"],"title_canon_sha256":"78260256a26a26fe9b1aa6c24b582bc57a41dbdbd04964be7ef5c108c0cff992","abstract_canon_sha256":"8ff1a908b14f6b40318f10da03f593255d6782c09b6be4868505af715a76b724"},"schema_version":"1.0"},"canonical_sha256":"3523b41d9dbc504f4d78d77095d90205dbe362b570cac934017b607a2d02a0ac","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:30:51.611836Z","signature_b64":"kUNlSOgwNMKq8locDUHdMxAZfunwQsEv+hm4GZMoOL0ghsqfgYwPyDE37YqAgfv+FNE6umUfA2RBpmuiWPH3Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3523b41d9dbc504f4d78d77095d90205dbe362b570cac934017b607a2d02a0ac","last_reissued_at":"2026-07-05T00:30:51.611300Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:30:51.611300Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.02945","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":"2026-07-05T00:30:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DsJ1qzetEHWvVq/w3JwFO53jZwXHJX89lJsRl3udl5bvcFSuFbvtD3u8ITzeVqV1mjpiiSGUYMow81YEl4w7AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T04:55:20.177678Z"},"content_sha256":"bfce19a21e46f88f51c9bc58bd27e017009533422897ea9dbb2ad933790eed9c","schema_version":"1.0","event_id":"sha256:bfce19a21e46f88f51c9bc58bd27e017009533422897ea9dbb2ad933790eed9c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:GUR3IHM5XRIE6TLY25YJLWICAX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lambert-W solves the noncommutative $\\Phi^4$-model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.CV","math.MP"],"primary_cat":"math-ph","authors_text":"Erik Panzer (Oxford), Raimar Wulkenhaar (M\\\"unster)","submitted_at":"2018-07-09T05:12:06Z","abstract_excerpt":"The closed Dyson-Schwinger equation for the 2-point function of the noncommutative $\\lambda \\phi^4_2$-model is rearranged into the boundary value problem for a sectionally holomorphic function in two variables. We prove an exact formula for a solution in terms of Lambert's $W$-function. This solution is holomorphic in $\\lambda$ inside a domain which contains $(-1/\\log 4,\\infty)$. Our methods include the Hilbert transform, perturbation series and Lagrange-B\\\"urmann resummation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.02945","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1807.02945/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":"2026-07-05T00:30:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7V9WwmpeEFjEflBhQBrL+ysp+tgJXpAIEurT4VbBDvVVB/AqqFmjsjs4Ty3JHlnccodIKYmk6DQdyqSmMpZ+Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T04:55:20.178349Z"},"content_sha256":"56dd0799107167713eb47e7393839b22d4af7bae49534303b7029666c5dbf975","schema_version":"1.0","event_id":"sha256:56dd0799107167713eb47e7393839b22d4af7bae49534303b7029666c5dbf975"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GUR3IHM5XRIE6TLY25YJLWICAX/bundle.json","state_url":"https://pith.science/pith/GUR3IHM5XRIE6TLY25YJLWICAX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GUR3IHM5XRIE6TLY25YJLWICAX/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":"2026-08-17T04:55:20Z","links":{"resolver":"https://pith.science/pith/GUR3IHM5XRIE6TLY25YJLWICAX","bundle":"https://pith.science/pith/GUR3IHM5XRIE6TLY25YJLWICAX/bundle.json","state":"https://pith.science/pith/GUR3IHM5XRIE6TLY25YJLWICAX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GUR3IHM5XRIE6TLY25YJLWICAX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:GUR3IHM5XRIE6TLY25YJLWICAX","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":"8ff1a908b14f6b40318f10da03f593255d6782c09b6be4868505af715a76b724","cross_cats_sorted":["hep-th","math.CV","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-07-09T05:12:06Z","title_canon_sha256":"78260256a26a26fe9b1aa6c24b582bc57a41dbdbd04964be7ef5c108c0cff992"},"schema_version":"1.0","source":{"id":"1807.02945","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.02945","created_at":"2026-07-05T00:30:51Z"},{"alias_kind":"arxiv_version","alias_value":"1807.02945v2","created_at":"2026-07-05T00:30:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.02945","created_at":"2026-07-05T00:30:51Z"},{"alias_kind":"pith_short_12","alias_value":"GUR3IHM5XRIE","created_at":"2026-07-05T00:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"GUR3IHM5XRIE6TLY","created_at":"2026-07-05T00:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"GUR3IHM5","created_at":"2026-07-05T00:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:56dd0799107167713eb47e7393839b22d4af7bae49534303b7029666c5dbf975","target":"graph","created_at":"2026-07-05T00:30:51Z","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/1807.02945/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The closed Dyson-Schwinger equation for the 2-point function of the noncommutative $\\lambda \\phi^4_2$-model is rearranged into the boundary value problem for a sectionally holomorphic function in two variables. We prove an exact formula for a solution in terms of Lambert's $W$-function. This solution is holomorphic in $\\lambda$ inside a domain which contains $(-1/\\log 4,\\infty)$. Our methods include the Hilbert transform, perturbation series and Lagrange-B\\\"urmann resummation.","authors_text":"Erik Panzer (Oxford), Raimar Wulkenhaar (M\\\"unster)","cross_cats":["hep-th","math.CV","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-07-09T05:12:06Z","title":"Lambert-W solves the noncommutative $\\Phi^4$-model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.02945","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:bfce19a21e46f88f51c9bc58bd27e017009533422897ea9dbb2ad933790eed9c","target":"record","created_at":"2026-07-05T00:30:51Z","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":"8ff1a908b14f6b40318f10da03f593255d6782c09b6be4868505af715a76b724","cross_cats_sorted":["hep-th","math.CV","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-07-09T05:12:06Z","title_canon_sha256":"78260256a26a26fe9b1aa6c24b582bc57a41dbdbd04964be7ef5c108c0cff992"},"schema_version":"1.0","source":{"id":"1807.02945","kind":"arxiv","version":2}},"canonical_sha256":"3523b41d9dbc504f4d78d77095d90205dbe362b570cac934017b607a2d02a0ac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3523b41d9dbc504f4d78d77095d90205dbe362b570cac934017b607a2d02a0ac","first_computed_at":"2026-07-05T00:30:51.611300Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:30:51.611300Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kUNlSOgwNMKq8locDUHdMxAZfunwQsEv+hm4GZMoOL0ghsqfgYwPyDE37YqAgfv+FNE6umUfA2RBpmuiWPH3Dw==","signature_status":"signed_v1","signed_at":"2026-07-05T00:30:51.611836Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.02945","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bfce19a21e46f88f51c9bc58bd27e017009533422897ea9dbb2ad933790eed9c","sha256:56dd0799107167713eb47e7393839b22d4af7bae49534303b7029666c5dbf975"],"state_sha256":"ae4a53acdbc8fd95c7c9aa920fdacfcf4cd47435e846f813187a0c8650876e96"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nZC9v3RjcxoSUtDJHkgHZ4JrkLvkKKTPuB5oEwHKw4qfrNI7sleYbjESF90s0p+0YHURejD2bNn10VlDz5yiBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T04:55:20.183694Z","bundle_sha256":"509b6f691bd2b4b12490f4ba5626fa6ca6776d9ff58746f776d1d9a1d783384e"}}