{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:6XETWQYGXCEHVFYFCF2JVFIAXA","short_pith_number":"pith:6XETWQYG","canonical_record":{"source":{"id":"1508.02575","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-08-11T12:34:55Z","cross_cats_sorted":[],"title_canon_sha256":"df352b4298193dfecc7f88c811fa7200d11aa96ab1ab42541530ea6e5f124d4e","abstract_canon_sha256":"cb443c0e5986a2f2405085a5168bd7e9e4ab81971e2cdf268d4d7d3e3e84b1a0"},"schema_version":"1.0"},"canonical_sha256":"f5c93b4306b8887a970511749a9500b834f4c866b27aec3d01483bee1867fd94","source":{"kind":"arxiv","id":"1508.02575","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.02575","created_at":"2026-05-18T01:29:29Z"},{"alias_kind":"arxiv_version","alias_value":"1508.02575v1","created_at":"2026-05-18T01:29:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.02575","created_at":"2026-05-18T01:29:29Z"},{"alias_kind":"pith_short_12","alias_value":"6XETWQYGXCEH","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6XETWQYGXCEHVFYF","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6XETWQYG","created_at":"2026-05-18T12:29:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:6XETWQYGXCEHVFYFCF2JVFIAXA","target":"record","payload":{"canonical_record":{"source":{"id":"1508.02575","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-08-11T12:34:55Z","cross_cats_sorted":[],"title_canon_sha256":"df352b4298193dfecc7f88c811fa7200d11aa96ab1ab42541530ea6e5f124d4e","abstract_canon_sha256":"cb443c0e5986a2f2405085a5168bd7e9e4ab81971e2cdf268d4d7d3e3e84b1a0"},"schema_version":"1.0"},"canonical_sha256":"f5c93b4306b8887a970511749a9500b834f4c866b27aec3d01483bee1867fd94","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:29:29.273668Z","signature_b64":"dRiRju/IGRIaRASn+w0LByTTQ9mBeKjm8QZ/SaWOIGCco1nW8+xrfGczYRUgCjc1DeTAI0VToj+8xqP+lrpbCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f5c93b4306b8887a970511749a9500b834f4c866b27aec3d01483bee1867fd94","last_reissued_at":"2026-05-18T01:29:29.273122Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:29:29.273122Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.02575","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:29:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Dk3P+Jd6Pli89GUiBZMpbEE3rPdAZfzingcsTY8wieZouIKEQoy0RQgSwxDP6gle7ze6CXLM8LPXkdwf7Ap/BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T17:53:37.568875Z"},"content_sha256":"3dee37befe2006cb7eaabfd5964e7ea242ab34e1f99b4fa0516d30873d8821af","schema_version":"1.0","event_id":"sha256:3dee37befe2006cb7eaabfd5964e7ea242ab34e1f99b4fa0516d30873d8821af"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:6XETWQYGXCEHVFYFCF2JVFIAXA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Green's Functions for Translation Invariant Star Products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Fedele Lizzi, Manolo Rivera, Patrizia Vitale","submitted_at":"2015-08-11T12:34:55Z","abstract_excerpt":"We calculate the Green functions for a scalar field theory with quartic interactions for which the fields are multiplied with a generic translation invariant star product. Our analysis involves both noncommutative products, for which there is the canonical commutation relation among coordinates, and nonlocal commutative products. We give explicit expressions for the one-loop corrections to the two and four point functions. We find that the phenomenon of ultraviolet/infrared mixing is always a consequence of the presence of noncommuting variables. The commutative part of the product does not ha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.02575","kind":"arxiv","version":1},"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":"2026-05-18T01:29:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nhGHboWFQU8oq3Gey8awQbbvca93qd80A75TjGk3OvgF+ciuqREA2HH9dBZV4OEDi+uoJTiVmwLnDErSdBHnBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T17:53:37.569277Z"},"content_sha256":"910fa00fe8287468cca9015c472b86f4e8a24dcf221d1b5ef97d0cc84880f730","schema_version":"1.0","event_id":"sha256:910fa00fe8287468cca9015c472b86f4e8a24dcf221d1b5ef97d0cc84880f730"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6XETWQYGXCEHVFYFCF2JVFIAXA/bundle.json","state_url":"https://pith.science/pith/6XETWQYGXCEHVFYFCF2JVFIAXA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6XETWQYGXCEHVFYFCF2JVFIAXA/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":"2026-05-29T17:53:37Z","links":{"resolver":"https://pith.science/pith/6XETWQYGXCEHVFYFCF2JVFIAXA","bundle":"https://pith.science/pith/6XETWQYGXCEHVFYFCF2JVFIAXA/bundle.json","state":"https://pith.science/pith/6XETWQYGXCEHVFYFCF2JVFIAXA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6XETWQYGXCEHVFYFCF2JVFIAXA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:6XETWQYGXCEHVFYFCF2JVFIAXA","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":"cb443c0e5986a2f2405085a5168bd7e9e4ab81971e2cdf268d4d7d3e3e84b1a0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-08-11T12:34:55Z","title_canon_sha256":"df352b4298193dfecc7f88c811fa7200d11aa96ab1ab42541530ea6e5f124d4e"},"schema_version":"1.0","source":{"id":"1508.02575","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.02575","created_at":"2026-05-18T01:29:29Z"},{"alias_kind":"arxiv_version","alias_value":"1508.02575v1","created_at":"2026-05-18T01:29:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.02575","created_at":"2026-05-18T01:29:29Z"},{"alias_kind":"pith_short_12","alias_value":"6XETWQYGXCEH","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6XETWQYGXCEHVFYF","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6XETWQYG","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:910fa00fe8287468cca9015c472b86f4e8a24dcf221d1b5ef97d0cc84880f730","target":"graph","created_at":"2026-05-18T01:29:29Z","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 calculate the Green functions for a scalar field theory with quartic interactions for which the fields are multiplied with a generic translation invariant star product. Our analysis involves both noncommutative products, for which there is the canonical commutation relation among coordinates, and nonlocal commutative products. We give explicit expressions for the one-loop corrections to the two and four point functions. We find that the phenomenon of ultraviolet/infrared mixing is always a consequence of the presence of noncommuting variables. The commutative part of the product does not ha","authors_text":"Fedele Lizzi, Manolo Rivera, Patrizia Vitale","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-08-11T12:34:55Z","title":"Green's Functions for Translation Invariant Star Products"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.02575","kind":"arxiv","version":1},"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":"sha256:3dee37befe2006cb7eaabfd5964e7ea242ab34e1f99b4fa0516d30873d8821af","target":"record","created_at":"2026-05-18T01:29:29Z","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":"cb443c0e5986a2f2405085a5168bd7e9e4ab81971e2cdf268d4d7d3e3e84b1a0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-08-11T12:34:55Z","title_canon_sha256":"df352b4298193dfecc7f88c811fa7200d11aa96ab1ab42541530ea6e5f124d4e"},"schema_version":"1.0","source":{"id":"1508.02575","kind":"arxiv","version":1}},"canonical_sha256":"f5c93b4306b8887a970511749a9500b834f4c866b27aec3d01483bee1867fd94","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f5c93b4306b8887a970511749a9500b834f4c866b27aec3d01483bee1867fd94","first_computed_at":"2026-05-18T01:29:29.273122Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:29:29.273122Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dRiRju/IGRIaRASn+w0LByTTQ9mBeKjm8QZ/SaWOIGCco1nW8+xrfGczYRUgCjc1DeTAI0VToj+8xqP+lrpbCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:29:29.273668Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.02575","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3dee37befe2006cb7eaabfd5964e7ea242ab34e1f99b4fa0516d30873d8821af","sha256:910fa00fe8287468cca9015c472b86f4e8a24dcf221d1b5ef97d0cc84880f730"],"state_sha256":"5beb73d7b7a77cd546846807ac51c351cc1366923a577c1689603a965220dbda"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oOqGMOPFOzpsIYA2kGtpF10oQ+gzhD1S4ciBQKFDKKI20z29Yu594HZUnFaFzGLzzW1VdhkkmXuBLhtH5b6TBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T17:53:37.572091Z","bundle_sha256":"85ee9427034a62bd3419ca6499f236a7045881f61d2c2600a773061f30d652eb"}}