{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:CRE5O3UNEXM462X3KFUKHXGKCV","short_pith_number":"pith:CRE5O3UN","canonical_record":{"source":{"id":"1404.5077","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-20T22:47:06Z","cross_cats_sorted":[],"title_canon_sha256":"3358cc83f00ca3fda3765d29270344acd1656d2d95c6aeb4f039b51f28e4fb86","abstract_canon_sha256":"6dc8b7234529bc75bf9b81511b1bac194dd1bca40497e25c19de8a0e69e65037"},"schema_version":"1.0"},"canonical_sha256":"1449d76e8d25d9cf6afb5168a3dcca155b0c7ea7cc26b0515c0b81834a95adcd","source":{"kind":"arxiv","id":"1404.5077","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.5077","created_at":"2026-05-18T01:11:41Z"},{"alias_kind":"arxiv_version","alias_value":"1404.5077v5","created_at":"2026-05-18T01:11:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.5077","created_at":"2026-05-18T01:11:41Z"},{"alias_kind":"pith_short_12","alias_value":"CRE5O3UNEXM4","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"CRE5O3UNEXM462X3","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"CRE5O3UN","created_at":"2026-05-18T12:28:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:CRE5O3UNEXM462X3KFUKHXGKCV","target":"record","payload":{"canonical_record":{"source":{"id":"1404.5077","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-20T22:47:06Z","cross_cats_sorted":[],"title_canon_sha256":"3358cc83f00ca3fda3765d29270344acd1656d2d95c6aeb4f039b51f28e4fb86","abstract_canon_sha256":"6dc8b7234529bc75bf9b81511b1bac194dd1bca40497e25c19de8a0e69e65037"},"schema_version":"1.0"},"canonical_sha256":"1449d76e8d25d9cf6afb5168a3dcca155b0c7ea7cc26b0515c0b81834a95adcd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:41.498103Z","signature_b64":"1SVyAyc1oDk+s3AGFAwar0XBIelu/MUb12jeEtOnNRh18SbNPBTJMZVsnwbBQxAy+qxn/wFGWjtEdHrl0+VeBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1449d76e8d25d9cf6afb5168a3dcca155b0c7ea7cc26b0515c0b81834a95adcd","last_reissued_at":"2026-05-18T01:11:41.497764Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:41.497764Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.5077","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:11:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IFnGXGKslux9X0eOHVfVB0d2AwinqOjX3W1ydYuEH6D63d/C0rXTIxRAF8YkjiVv/I1UUm3+U5qw3+hXFDscBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T20:37:25.496307Z"},"content_sha256":"e618ec6141c131a1175cdae1b91597fde1e3553dfa47fd49cff49b7e23ed7cc8","schema_version":"1.0","event_id":"sha256:e618ec6141c131a1175cdae1b91597fde1e3553dfa47fd49cff49b7e23ed7cc8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:CRE5O3UNEXM462X3KFUKHXGKCV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A doubly nonlinear evolution for the optimal Poincar\\'e inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Erik Lindgren, Ryan Hynd","submitted_at":"2014-04-20T22:47:06Z","abstract_excerpt":"We study the large time behavior of solutions of the PDE $|v_t|^{p-2}v_t=\\Delta_p v$. A special property of this equation is that the Rayleigh quotient $\\int_{\\Omega}|Dv(x,t)|^pdx /\\int_{\\Omega}|v(x,t)|^pdx$ is nonincreasing in time along solutions. As $t$ tends to infinity, this ratio converges to the optimal constant in Poincar\\'{e}'s inequality. Moreover, appropriately scaled solutions converge to a function for which equality holds in this inequality. An interesting limiting equation also arises when $p$ tends to infinity, which provides a new approach to approximating ground states of the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5077","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:11:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OyoF9s2Z9BR7GbAYMBph7ZHory0/Ag7y1wd/YcCP9CzgUux9SqMe2vd0iG8Xz1x4YwDhrHuaY5vexCmkw1cICA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T20:37:25.496674Z"},"content_sha256":"8b35b0f13ad9cc5dd6d00385a975ece4881aa6448f015b7531310257c3668475","schema_version":"1.0","event_id":"sha256:8b35b0f13ad9cc5dd6d00385a975ece4881aa6448f015b7531310257c3668475"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CRE5O3UNEXM462X3KFUKHXGKCV/bundle.json","state_url":"https://pith.science/pith/CRE5O3UNEXM462X3KFUKHXGKCV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CRE5O3UNEXM462X3KFUKHXGKCV/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-20T20:37:25Z","links":{"resolver":"https://pith.science/pith/CRE5O3UNEXM462X3KFUKHXGKCV","bundle":"https://pith.science/pith/CRE5O3UNEXM462X3KFUKHXGKCV/bundle.json","state":"https://pith.science/pith/CRE5O3UNEXM462X3KFUKHXGKCV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CRE5O3UNEXM462X3KFUKHXGKCV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:CRE5O3UNEXM462X3KFUKHXGKCV","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":"6dc8b7234529bc75bf9b81511b1bac194dd1bca40497e25c19de8a0e69e65037","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-20T22:47:06Z","title_canon_sha256":"3358cc83f00ca3fda3765d29270344acd1656d2d95c6aeb4f039b51f28e4fb86"},"schema_version":"1.0","source":{"id":"1404.5077","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.5077","created_at":"2026-05-18T01:11:41Z"},{"alias_kind":"arxiv_version","alias_value":"1404.5077v5","created_at":"2026-05-18T01:11:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.5077","created_at":"2026-05-18T01:11:41Z"},{"alias_kind":"pith_short_12","alias_value":"CRE5O3UNEXM4","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"CRE5O3UNEXM462X3","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"CRE5O3UN","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:8b35b0f13ad9cc5dd6d00385a975ece4881aa6448f015b7531310257c3668475","target":"graph","created_at":"2026-05-18T01:11:41Z","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 study the large time behavior of solutions of the PDE $|v_t|^{p-2}v_t=\\Delta_p v$. A special property of this equation is that the Rayleigh quotient $\\int_{\\Omega}|Dv(x,t)|^pdx /\\int_{\\Omega}|v(x,t)|^pdx$ is nonincreasing in time along solutions. As $t$ tends to infinity, this ratio converges to the optimal constant in Poincar\\'{e}'s inequality. Moreover, appropriately scaled solutions converge to a function for which equality holds in this inequality. An interesting limiting equation also arises when $p$ tends to infinity, which provides a new approach to approximating ground states of the","authors_text":"Erik Lindgren, Ryan Hynd","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-20T22:47:06Z","title":"A doubly nonlinear evolution for the optimal Poincar\\'e inequality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5077","kind":"arxiv","version":5},"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:e618ec6141c131a1175cdae1b91597fde1e3553dfa47fd49cff49b7e23ed7cc8","target":"record","created_at":"2026-05-18T01:11:41Z","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":"6dc8b7234529bc75bf9b81511b1bac194dd1bca40497e25c19de8a0e69e65037","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-20T22:47:06Z","title_canon_sha256":"3358cc83f00ca3fda3765d29270344acd1656d2d95c6aeb4f039b51f28e4fb86"},"schema_version":"1.0","source":{"id":"1404.5077","kind":"arxiv","version":5}},"canonical_sha256":"1449d76e8d25d9cf6afb5168a3dcca155b0c7ea7cc26b0515c0b81834a95adcd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1449d76e8d25d9cf6afb5168a3dcca155b0c7ea7cc26b0515c0b81834a95adcd","first_computed_at":"2026-05-18T01:11:41.497764Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:41.497764Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1SVyAyc1oDk+s3AGFAwar0XBIelu/MUb12jeEtOnNRh18SbNPBTJMZVsnwbBQxAy+qxn/wFGWjtEdHrl0+VeBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:41.498103Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.5077","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e618ec6141c131a1175cdae1b91597fde1e3553dfa47fd49cff49b7e23ed7cc8","sha256:8b35b0f13ad9cc5dd6d00385a975ece4881aa6448f015b7531310257c3668475"],"state_sha256":"e82365a318664affcecdb512965bad1ff1e71f8a6b4c32ae0becc531e5363b5f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y/xTAWI2mvty9sFDz/e8D69XDdSea2lua/9VkYzU9i4zV6fkj7bRaZCmh9tSBfB4M8kC1hpvq1b2hQ0sPUpBAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T20:37:25.498592Z","bundle_sha256":"e62246bfeab85a793caa738ec0babc8265b551458c0e351a8830570db5e165b6"}}