{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:YDIQM2DJKV4VXY3UW3SWVMQWNE","short_pith_number":"pith:YDIQM2DJ","canonical_record":{"source":{"id":"2608.13443","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-08-13T16:29:36Z","cross_cats_sorted":[],"title_canon_sha256":"f62ac9a5fa475b7d2b29ad2d486066a051f4327ed5894cc49a969aad05067402","abstract_canon_sha256":"b328bee107e813623433ad4cb5608ad7c11988391018d4608829c8cdac62b84e"},"schema_version":"1.0"},"canonical_sha256":"c0d106686955795be374b6e56ab2166917f0878d9851ec34c9d7cc7a172f2f96","source":{"kind":"arxiv","id":"2608.13443","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.13443","created_at":"2026-08-14T01:04:27Z"},{"alias_kind":"arxiv_version","alias_value":"2608.13443v1","created_at":"2026-08-14T01:04:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.13443","created_at":"2026-08-14T01:04:27Z"},{"alias_kind":"pith_short_12","alias_value":"YDIQM2DJKV4V","created_at":"2026-08-14T01:04:27Z"},{"alias_kind":"pith_short_16","alias_value":"YDIQM2DJKV4VXY3U","created_at":"2026-08-14T01:04:27Z"},{"alias_kind":"pith_short_8","alias_value":"YDIQM2DJ","created_at":"2026-08-14T01:04:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:YDIQM2DJKV4VXY3UW3SWVMQWNE","target":"record","payload":{"canonical_record":{"source":{"id":"2608.13443","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-08-13T16:29:36Z","cross_cats_sorted":[],"title_canon_sha256":"f62ac9a5fa475b7d2b29ad2d486066a051f4327ed5894cc49a969aad05067402","abstract_canon_sha256":"b328bee107e813623433ad4cb5608ad7c11988391018d4608829c8cdac62b84e"},"schema_version":"1.0"},"canonical_sha256":"c0d106686955795be374b6e56ab2166917f0878d9851ec34c9d7cc7a172f2f96","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-14T01:04:27.205185Z","signature_b64":"Lz3lWQD+CI6X+s9r3fsvHkR5SmoccfDYTeMIy8jmdpC6UMVix4eQkRPa9qAS8s90LGkqsiqAyuFCv7IkYZWtBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c0d106686955795be374b6e56ab2166917f0878d9851ec34c9d7cc7a172f2f96","last_reissued_at":"2026-08-14T01:04:27.203469Z","signature_status":"signed_v1","first_computed_at":"2026-08-14T01:04:27.203469Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2608.13443","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-08-14T01:04:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SSKE5OmDU6nnT8PEgKyICU669T0j7r6urFcauUmpsYE0aTfP0zb64gQ6lqPHyPHkjbEEaVwuGhb/Bnhi7xCtDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T07:43:12.584154Z"},"content_sha256":"aac6fcaf8498093667ca69ba2bcd01f046223c1e8bff958de963ef223ac91700","schema_version":"1.0","event_id":"sha256:aac6fcaf8498093667ca69ba2bcd01f046223c1e8bff958de963ef223ac91700"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:YDIQM2DJKV4VXY3UW3SWVMQWNE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fundamental Gaps for the Dirichlet \\(p\\)-Laplacian with Convex Potentials: Sharp One-Dimensional Bounds and a Higher-Dimensional Dichotomy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Daniel Hauer, Rui Chen","submitted_at":"2026-08-13T16:29:36Z","abstract_excerpt":"We study fundamental gaps for the Dirichlet \\(p\\)-Laplacian on bounded convex domains with convex potentials. We prove log-concavity of the positive first eigenfunction by a regularization and two-point maximum principle. For \\(N\\geq2\\), we identify a sharp transition at \\(p=2\\) through collapsing smooth convex domains: the gap vanishes for \\(1<p<2\\), remains of order \\(D^{-2}\\) for \\(p=2\\), and diverges for \\(p>2\\). For \\(p\\geq2\\) and convex potentials, we first establish a degenerate weighted Poincar\\'e inequality, which yields quantitative stability estimates for the \\(L^p\\)-Poincar\\'e ineq"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.13443","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.13443/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-08-14T01:04:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c/uEzPHsjvM37ukyWHqU1I1kQnyn8iZUJY6kdP2DSKjZEt6h/DGsgriCJlK5fvyRzpT8RTBdmEXfNqLR8ZeACQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T07:43:12.584670Z"},"content_sha256":"e1d19721175f4cd511b51f4166165a8fbdc4363c8090c1fe53918db0bc7eff0a","schema_version":"1.0","event_id":"sha256:e1d19721175f4cd511b51f4166165a8fbdc4363c8090c1fe53918db0bc7eff0a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YDIQM2DJKV4VXY3UW3SWVMQWNE/bundle.json","state_url":"https://pith.science/pith/YDIQM2DJKV4VXY3UW3SWVMQWNE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YDIQM2DJKV4VXY3UW3SWVMQWNE/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":"2026-08-16T07:43:12Z","links":{"resolver":"https://pith.science/pith/YDIQM2DJKV4VXY3UW3SWVMQWNE","bundle":"https://pith.science/pith/YDIQM2DJKV4VXY3UW3SWVMQWNE/bundle.json","state":"https://pith.science/pith/YDIQM2DJKV4VXY3UW3SWVMQWNE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YDIQM2DJKV4VXY3UW3SWVMQWNE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:YDIQM2DJKV4VXY3UW3SWVMQWNE","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":"b328bee107e813623433ad4cb5608ad7c11988391018d4608829c8cdac62b84e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-08-13T16:29:36Z","title_canon_sha256":"f62ac9a5fa475b7d2b29ad2d486066a051f4327ed5894cc49a969aad05067402"},"schema_version":"1.0","source":{"id":"2608.13443","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.13443","created_at":"2026-08-14T01:04:27Z"},{"alias_kind":"arxiv_version","alias_value":"2608.13443v1","created_at":"2026-08-14T01:04:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.13443","created_at":"2026-08-14T01:04:27Z"},{"alias_kind":"pith_short_12","alias_value":"YDIQM2DJKV4V","created_at":"2026-08-14T01:04:27Z"},{"alias_kind":"pith_short_16","alias_value":"YDIQM2DJKV4VXY3U","created_at":"2026-08-14T01:04:27Z"},{"alias_kind":"pith_short_8","alias_value":"YDIQM2DJ","created_at":"2026-08-14T01:04:27Z"}],"graph_snapshots":[{"event_id":"sha256:e1d19721175f4cd511b51f4166165a8fbdc4363c8090c1fe53918db0bc7eff0a","target":"graph","created_at":"2026-08-14T01:04:27Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2608.13443/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study fundamental gaps for the Dirichlet \\(p\\)-Laplacian on bounded convex domains with convex potentials. We prove log-concavity of the positive first eigenfunction by a regularization and two-point maximum principle. For \\(N\\geq2\\), we identify a sharp transition at \\(p=2\\) through collapsing smooth convex domains: the gap vanishes for \\(1<p<2\\), remains of order \\(D^{-2}\\) for \\(p=2\\), and diverges for \\(p>2\\). For \\(p\\geq2\\) and convex potentials, we first establish a degenerate weighted Poincar\\'e inequality, which yields quantitative stability estimates for the \\(L^p\\)-Poincar\\'e ineq","authors_text":"Daniel Hauer, Rui Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-08-13T16:29:36Z","title":"Fundamental Gaps for the Dirichlet \\(p\\)-Laplacian with Convex Potentials: Sharp One-Dimensional Bounds and a Higher-Dimensional Dichotomy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.13443","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:aac6fcaf8498093667ca69ba2bcd01f046223c1e8bff958de963ef223ac91700","target":"record","created_at":"2026-08-14T01:04:27Z","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":"b328bee107e813623433ad4cb5608ad7c11988391018d4608829c8cdac62b84e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-08-13T16:29:36Z","title_canon_sha256":"f62ac9a5fa475b7d2b29ad2d486066a051f4327ed5894cc49a969aad05067402"},"schema_version":"1.0","source":{"id":"2608.13443","kind":"arxiv","version":1}},"canonical_sha256":"c0d106686955795be374b6e56ab2166917f0878d9851ec34c9d7cc7a172f2f96","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c0d106686955795be374b6e56ab2166917f0878d9851ec34c9d7cc7a172f2f96","first_computed_at":"2026-08-14T01:04:27.203469Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-14T01:04:27.203469Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Lz3lWQD+CI6X+s9r3fsvHkR5SmoccfDYTeMIy8jmdpC6UMVix4eQkRPa9qAS8s90LGkqsiqAyuFCv7IkYZWtBQ==","signature_status":"signed_v1","signed_at":"2026-08-14T01:04:27.205185Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.13443","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aac6fcaf8498093667ca69ba2bcd01f046223c1e8bff958de963ef223ac91700","sha256:e1d19721175f4cd511b51f4166165a8fbdc4363c8090c1fe53918db0bc7eff0a"],"state_sha256":"c40ef19385e1195acfbd2a015e8a9b324c1a12a2d458d7824d0a59edd52a5d4e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s+fGYTfgw2kgyNHgKhhqTAwp8eg1TMTNqLNaQUkQxgZlrU6soKWPKaLb2osUXwXTQD4aUZ8mwXWg/mbIHoXeBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T07:43:12.588466Z","bundle_sha256":"82321c6b10e7adc289a46b160aecb3985f78a6fb0d8cbaa1b9b0d00b8a10e320"}}