{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:2Y65TZVA7JJKR7BYX6FIAXPALJ","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":"9d431f5f9a38f412cc4e2dbc9223b9f267b8755c2b0c28d33c94686e84dcb741","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-07-07T04:24:02Z","title_canon_sha256":"c72cd97b0d4dbbf48f9263011ee009ff98d0e9b9f094f3dfa1610047abe0997a"},"schema_version":"1.0","source":{"id":"1607.01871","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.01871","created_at":"2026-05-18T00:57:11Z"},{"alias_kind":"arxiv_version","alias_value":"1607.01871v1","created_at":"2026-05-18T00:57:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.01871","created_at":"2026-05-18T00:57:11Z"},{"alias_kind":"pith_short_12","alias_value":"2Y65TZVA7JJK","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2Y65TZVA7JJKR7BY","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2Y65TZVA","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:c94e3a277d65b6bb00eda9185b1894db8997018fd846836c44781efbafc4f968","target":"graph","created_at":"2026-05-18T00:57:11Z","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":"Recently, we proposed a new approach using a punctured Elliptic curve in the CHY framework in order to compute one-loop scattering amplitudes. In this note, we further develop this approach by introducing a set of connectors, which become the main ingredient to build integrands on $\\mathfrak{M}_{1,n}$, the moduli space of n-punctured Elliptic curves. As a particular application, we study the $\\Phi^3$ bi-adjoint scalar theory. We propose a set of rules to construct integrands on $\\mathfrak{M}_{1,n}$ from $\\Phi^ 3$ integrands on $\\mathfrak{M}_{0,n}$, the moduli space of n-punctured spheres. We i","authors_text":"Carlos Cardona, Humberto Gomez","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-07-07T04:24:02Z","title":"CHY-Graphs on a Torus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.01871","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:d2c2df4184e6844d1300149847ce162f34fd8c043eba36220d65fe353cc7ef4b","target":"record","created_at":"2026-05-18T00:57:11Z","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":"9d431f5f9a38f412cc4e2dbc9223b9f267b8755c2b0c28d33c94686e84dcb741","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-07-07T04:24:02Z","title_canon_sha256":"c72cd97b0d4dbbf48f9263011ee009ff98d0e9b9f094f3dfa1610047abe0997a"},"schema_version":"1.0","source":{"id":"1607.01871","kind":"arxiv","version":1}},"canonical_sha256":"d63dd9e6a0fa52a8fc38bf8a805de05a6e8ef47042ef94c463aa8eafbb80ae60","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d63dd9e6a0fa52a8fc38bf8a805de05a6e8ef47042ef94c463aa8eafbb80ae60","first_computed_at":"2026-05-18T00:57:11.887593Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:11.887593Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iX1CltxNFrZmpBQsNouDSd62121slNH2h1SQ5sObCftkH+BoJn0w4og4ndW2hg3Dlp/TOP66qZSzdCPZsX0AAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:11.888005Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.01871","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d2c2df4184e6844d1300149847ce162f34fd8c043eba36220d65fe353cc7ef4b","sha256:c94e3a277d65b6bb00eda9185b1894db8997018fd846836c44781efbafc4f968"],"state_sha256":"3df146e2df479bc6cad55f650c4ad70933fce677c9bac039e3eeaf44ff17ba2f"}