{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:MVVE6ZTPZ7MIAPGPJKZ5JLVCHL","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":"b9e437f68d3ddd63c95c3a1ca64c79f2ee1c5201933c59cab4ce45131139e823","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-01-14T18:52:24Z","title_canon_sha256":"b893c8b91ae656d9b939296ec42ec943775ec36c5ea357f94231aa616bb86a52"},"schema_version":"1.0","source":{"id":"1101.2873","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.2873","created_at":"2026-05-18T04:31:31Z"},{"alias_kind":"arxiv_version","alias_value":"1101.2873v1","created_at":"2026-05-18T04:31:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.2873","created_at":"2026-05-18T04:31:31Z"},{"alias_kind":"pith_short_12","alias_value":"MVVE6ZTPZ7MI","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"MVVE6ZTPZ7MIAPGP","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"MVVE6ZTP","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:0b9f8a5d4f36afb5266805263884da68192c41e082ed10cccae9fe02f52f87d9","target":"graph","created_at":"2026-05-18T04:31:31Z","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 prove that the Green equilibrium measure and the Green equilibrium energy of a compact set K relative to the domains D and G are the same if and only if D is nearly equal to G, for a wide class of compact sets K. Also, we prove that equality of Green equilibrium measures arises if and only if the one domain is related with a level set of the Green equilibrium potential of K relative to the other domain.","authors_text":"Stamatis Pouliasis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-01-14T18:52:24Z","title":"Invariance of Green equilibrium measure on the domain"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.2873","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":"sha256:01b2ff9f96b9d37a1abbb87c6ee3bf788222f2c57b73a046187da64875fc9cd8","target":"record","created_at":"2026-05-18T04:31:31Z","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":"b9e437f68d3ddd63c95c3a1ca64c79f2ee1c5201933c59cab4ce45131139e823","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-01-14T18:52:24Z","title_canon_sha256":"b893c8b91ae656d9b939296ec42ec943775ec36c5ea357f94231aa616bb86a52"},"schema_version":"1.0","source":{"id":"1101.2873","kind":"arxiv","version":1}},"canonical_sha256":"656a4f666fcfd8803ccf4ab3d4aea23adaea1c1bfa275eaa5729488f7129e5d9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"656a4f666fcfd8803ccf4ab3d4aea23adaea1c1bfa275eaa5729488f7129e5d9","first_computed_at":"2026-05-18T04:31:31.650847Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:31:31.650847Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A5FCZ7DkNJIpqUlcKWI81AD0mYUMV8eaQVafiNuoHFgr7Cy6TqtfLTVvAUyvFAw528xcWUzqoxEH2qrg0s8vCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:31:31.651387Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.2873","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:01b2ff9f96b9d37a1abbb87c6ee3bf788222f2c57b73a046187da64875fc9cd8","sha256:0b9f8a5d4f36afb5266805263884da68192c41e082ed10cccae9fe02f52f87d9"],"state_sha256":"7253103a3d1aaae37ffe362475d6a82122753dce17ff41c479d42545f2d4e87a"}