{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:JW4WMEME4BAYFTKBRP57ZDB5L6","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":"29d836123e1636a618f5aec33de067b921aa132a615e45c6f35e661965a900c2","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-12-27T21:47:27Z","title_canon_sha256":"3953a6ef4fb2ba4de96315468e1652bb7ac5eed155644d780313264ef0087e71"},"schema_version":"1.0","source":{"id":"1012.5672","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.5672","created_at":"2026-05-18T04:32:22Z"},{"alias_kind":"arxiv_version","alias_value":"1012.5672v1","created_at":"2026-05-18T04:32:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.5672","created_at":"2026-05-18T04:32:22Z"},{"alias_kind":"pith_short_12","alias_value":"JW4WMEME4BAY","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"JW4WMEME4BAYFTKB","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"JW4WMEME","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:649401b43a09ef200c40b256ff483821e0abeee23af3469a16be57f58497f2dc","target":"graph","created_at":"2026-05-18T04:32:22Z","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":"Given (M, g0) we consider the problem -{\\epsilon}^2Delta_{g0+h}u + u = (u+)^{p-1} with ({\\epsilon}, h) \\in (0, {\\epsilon}0) \\times B{\\rho}. Here B{\\rho} is a ball centered at 0 with radius {\\rho} in the Banach space of all Ck symmetric covariant 2-tensors on M. Using the Poincar\\'e polynomial of M, we give an estimate on the number of nonconstant solutions with low energy for ({\\epsilon}, h) belonging to a residual subset of (0, {\\epsilon}0) \\times B{\\rho}, for ({\\epsilon}0, {\\rho}) small enough.","authors_text":"Anna Maria Micheletti, Marco G. Ghimenti","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-12-27T21:47:27Z","title":"Positive solutions for singularly perturbed nonlinear elliptic problem on manifolds via Morse theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.5672","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:f1f77868cbb294608cea1218f82d090fd66445298871e33d43b824a2da590784","target":"record","created_at":"2026-05-18T04:32:22Z","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":"29d836123e1636a618f5aec33de067b921aa132a615e45c6f35e661965a900c2","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-12-27T21:47:27Z","title_canon_sha256":"3953a6ef4fb2ba4de96315468e1652bb7ac5eed155644d780313264ef0087e71"},"schema_version":"1.0","source":{"id":"1012.5672","kind":"arxiv","version":1}},"canonical_sha256":"4db9661184e04182cd418bfbfc8c3d5fbe2abac7c13fd12ee3d893b3d08d777c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4db9661184e04182cd418bfbfc8c3d5fbe2abac7c13fd12ee3d893b3d08d777c","first_computed_at":"2026-05-18T04:32:22.595445Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:32:22.595445Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O7el2QZDMfEXDpgYvasVKTTguXlMj5UCQetR/pbQ03hEu2PRbtcGW4LARAI2e6rF9B4uiBwx8a45xO3YD0d2AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:32:22.595986Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.5672","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f1f77868cbb294608cea1218f82d090fd66445298871e33d43b824a2da590784","sha256:649401b43a09ef200c40b256ff483821e0abeee23af3469a16be57f58497f2dc"],"state_sha256":"91f6ef38c9b3922eb8370f989f19467c011bf6a550e0f06d8e9be2fab620adf3"}