{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:ARV3QWET23JPOWFP5TKV4SDXL7","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":"e57cb95de509a3d78db62818dc79e081f09c67640c76c590969a0940042cb9d0","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-14T11:58:32Z","title_canon_sha256":"0e53386e1eb574f446d7587f17df114afb08c3a3fa8e6fff0c0e4effacce3a80"},"schema_version":"1.0","source":{"id":"2607.12671","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.12671","created_at":"2026-07-15T01:22:11Z"},{"alias_kind":"arxiv_version","alias_value":"2607.12671v1","created_at":"2026-07-15T01:22:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.12671","created_at":"2026-07-15T01:22:11Z"},{"alias_kind":"pith_short_12","alias_value":"ARV3QWET23JP","created_at":"2026-07-15T01:22:11Z"},{"alias_kind":"pith_short_16","alias_value":"ARV3QWET23JPOWFP","created_at":"2026-07-15T01:22:11Z"},{"alias_kind":"pith_short_8","alias_value":"ARV3QWET","created_at":"2026-07-15T01:22:11Z"}],"graph_snapshots":[{"event_id":"sha256:ba3be78e6d6197cf840b3efc1204cb3d4582dceebe1254e3ce80185fe42309c4","target":"graph","created_at":"2026-07-15T01:22:11Z","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/2607.12671/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For the two-dimensional Aharonov-Bohm potential $A_\\beta$ with flux $\\beta\\notin\\mathbb{Z}$ and $1<p<2$, Cazacu, Krej\\v{c}i\\v{r}\\'{\\i}k, Lam and Laptev proved by a compactness argument that their constant $\\lambda_\\beta(p)$ in the $L^p$-Hardy inequality strictly exceeds the free constant $\\big(\\tfrac{2-p}{p}\\big)^p$, and asked for a constructive proof with explicit estimates and for comparability of $\\lambda_\\beta(p)$ with a quantity depending on $\\text{dist}(\\beta,\\mathbb{Z})$. We answer both questions by using a compactness-free two-sided bound for the twisted angular constant. Our explicit ","authors_text":"Durvudkhan Suragan","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-14T11:58:32Z","title":"Explicit constants in $L^p$-Hardy inequalities for Aharonov-Bohm potentials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.12671","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":"sha256:450da892d7e16f2bad10732b507d76e807bd34f35f455411138e565dd346aaec","target":"record","created_at":"2026-07-15T01:22:11Z","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":"e57cb95de509a3d78db62818dc79e081f09c67640c76c590969a0940042cb9d0","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-14T11:58:32Z","title_canon_sha256":"0e53386e1eb574f446d7587f17df114afb08c3a3fa8e6fff0c0e4effacce3a80"},"schema_version":"1.0","source":{"id":"2607.12671","kind":"arxiv","version":1}},"canonical_sha256":"046bb85893d6d2f758afecd55e48775fd9c05f471b65063b0f66abfdffff3478","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"046bb85893d6d2f758afecd55e48775fd9c05f471b65063b0f66abfdffff3478","first_computed_at":"2026-07-15T01:22:11.300980Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-15T01:22:11.300980Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hZhNRmPJkEFJLOu25yWDEGCZdhSK5SqtTgVrm34fQjTywZFWPEVic2y64JD16fgx/gCg5/2s8TGudGsLPEvLAA==","signature_status":"signed_v1","signed_at":"2026-07-15T01:22:11.301937Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.12671","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:450da892d7e16f2bad10732b507d76e807bd34f35f455411138e565dd346aaec","sha256:ba3be78e6d6197cf840b3efc1204cb3d4582dceebe1254e3ce80185fe42309c4"],"state_sha256":"8755f81350c81c40b4e0d2c8564a2420ac367e1485ecd54e2354c0730adc75c1"}