{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:7GGIL5A72KWQAFOW3VJJNALACW","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":"d7eb6554518e15dd7b38d656809147eb14a610541a75a436d2209ea35312aa6d","cross_cats_sorted":["math.DS","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-23T14:28:44Z","title_canon_sha256":"9ead29a55f8c6130f994716cee8d299a55a9a0d2a9a1ee9f783a6685cd864631"},"schema_version":"1.0","source":{"id":"1601.06271","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.06271","created_at":"2026-05-18T00:53:12Z"},{"alias_kind":"arxiv_version","alias_value":"1601.06271v3","created_at":"2026-05-18T00:53:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.06271","created_at":"2026-05-18T00:53:12Z"},{"alias_kind":"pith_short_12","alias_value":"7GGIL5A72KWQ","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7GGIL5A72KWQAFOW","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7GGIL5A7","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:52242b60ab5c97681fbb42b664646a7f87da79a8e7893d3f8fdff15d5de3b8da","target":"graph","created_at":"2026-05-18T00:53:12Z","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 investigate minimal solutions of the Allen-Cahn equation on a Gromov-hyperbolic graph. Under some natural conditions on the graph, we show the existence of non-constant uniformly-bounded minimal solutions with prescribed asymptotic behaviours. For a phase field model on a hyperbolic graph, such solutions describe energy-minimising steady-state phase transitions that converge towards prescribed phases given by the asymptotic directions on the graph.","authors_text":"Blaz Mramor","cross_cats":["math.DS","math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-23T14:28:44Z","title":"Minimisers of the Allen-Cahn equation on hyperbolic graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.06271","kind":"arxiv","version":3},"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:e6d9b687e98249583a620c09014240baa271e0e9aceaf6a256427384b6b69787","target":"record","created_at":"2026-05-18T00:53:12Z","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":"d7eb6554518e15dd7b38d656809147eb14a610541a75a436d2209ea35312aa6d","cross_cats_sorted":["math.DS","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-23T14:28:44Z","title_canon_sha256":"9ead29a55f8c6130f994716cee8d299a55a9a0d2a9a1ee9f783a6685cd864631"},"schema_version":"1.0","source":{"id":"1601.06271","kind":"arxiv","version":3}},"canonical_sha256":"f98c85f41fd2ad0015d6dd5296816015a404be84ff94535811b1f897d4bedbef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f98c85f41fd2ad0015d6dd5296816015a404be84ff94535811b1f897d4bedbef","first_computed_at":"2026-05-18T00:53:12.454140Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:12.454140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ayv55OuwAj4/+BnYXMUjOlcCerN+F0upZQIH6WDXfmgCdmXhYIZ5WbIaDF8evsAUUGU67lkb3E4UF0MEXhv1CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:12.454631Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.06271","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e6d9b687e98249583a620c09014240baa271e0e9aceaf6a256427384b6b69787","sha256:52242b60ab5c97681fbb42b664646a7f87da79a8e7893d3f8fdff15d5de3b8da"],"state_sha256":"d7c8fe3bc611cab0c503d97fa59280c9e8bbf2c48d64d8253713886c80110433"}