{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:TEQ3CRZEAQAO2LULFJNLFEKDCX","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":"e764c13fb67cea08081cd1a363455d59f600ef01e12ec47b5d0951d75b96b680","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2013-08-08T13:06:08Z","title_canon_sha256":"ada28aae522d6436e8ee1f55f23ae4fc112145540d7c007b37fbf071da02c39b"},"schema_version":"1.0","source":{"id":"1308.1836","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.1836","created_at":"2026-05-18T03:12:08Z"},{"alias_kind":"arxiv_version","alias_value":"1308.1836v2","created_at":"2026-05-18T03:12:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.1836","created_at":"2026-05-18T03:12:08Z"},{"alias_kind":"pith_short_12","alias_value":"TEQ3CRZEAQAO","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"TEQ3CRZEAQAO2LUL","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"TEQ3CRZE","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:2bc210d69ad9136017fd582a05a6e281c904719cd4892461e8204b4791956f51","target":"graph","created_at":"2026-05-18T03:12:08Z","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":"A variational method is discussed, extending the Gaussian effective potential to higher orders. The single variational parameter is replaced by trial unknown two-point functions, with infinite variational parameters to be optimized by the solution of a set of integral equations. These stationary conditions are derived by the self-energy without having to write the effective potential, making use of a general relation between self-energy and functional derivatives of the potential. This connection is proven to any order and verified up to second order by an explicit calculation for the scalar t","authors_text":"Fabio Siringo","cross_cats":["hep-th","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2013-08-08T13:06:08Z","title":"Higher order extensions of the Gaussian effective potential"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.1836","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":"sha256:0a14049ef2eeac36615357458e6aceca77f7521f69cb13500916dc914c1eda62","target":"record","created_at":"2026-05-18T03:12:08Z","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":"e764c13fb67cea08081cd1a363455d59f600ef01e12ec47b5d0951d75b96b680","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2013-08-08T13:06:08Z","title_canon_sha256":"ada28aae522d6436e8ee1f55f23ae4fc112145540d7c007b37fbf071da02c39b"},"schema_version":"1.0","source":{"id":"1308.1836","kind":"arxiv","version":2}},"canonical_sha256":"9921b147240400ed2e8b2a5ab2914315eefe5e34617ed20ecf6df372ece76244","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9921b147240400ed2e8b2a5ab2914315eefe5e34617ed20ecf6df372ece76244","first_computed_at":"2026-05-18T03:12:08.420755Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:12:08.420755Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cd3/wVf6CSXSKHBjjT1LdgnciW419G02VKWWC7OnXvD3nNp+SNGHsPoteeiY3u932SusKqDandlYC3Lvw7qPDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:12:08.421563Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.1836","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0a14049ef2eeac36615357458e6aceca77f7521f69cb13500916dc914c1eda62","sha256:2bc210d69ad9136017fd582a05a6e281c904719cd4892461e8204b4791956f51"],"state_sha256":"6636f6b9007c43d6a3dd5241a4919fc2343a575b86f8fe75cfa9e85bc57d2322"}