{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:3LOBGPQWDT5ALQGLBDT5LSXLWL","short_pith_number":"pith:3LOBGPQW","canonical_record":{"source":{"id":"1906.03419","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-06-08T08:46:07Z","cross_cats_sorted":["math-ph","math.FA","math.MP","math.SP"],"title_canon_sha256":"af86569e5eec77bfdfae9b1a275cda004f3c8d0d098f18dc3b57ad219a496e74","abstract_canon_sha256":"dce8750387bbefe0af57bebf0ac53971ba0b18675c3d971840d34e1a1ee741da"},"schema_version":"1.0"},"canonical_sha256":"dadc133e161cfa05c0cb08e7d5caebb2ef9ebee1df45bc6c7877bb68aa523baa","source":{"kind":"arxiv","id":"1906.03419","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.03419","created_at":"2026-05-17T23:43:48Z"},{"alias_kind":"arxiv_version","alias_value":"1906.03419v1","created_at":"2026-05-17T23:43:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.03419","created_at":"2026-05-17T23:43:48Z"},{"alias_kind":"pith_short_12","alias_value":"3LOBGPQWDT5A","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"3LOBGPQWDT5ALQGL","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"3LOBGPQW","created_at":"2026-05-18T12:33:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:3LOBGPQWDT5ALQGLBDT5LSXLWL","target":"record","payload":{"canonical_record":{"source":{"id":"1906.03419","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-06-08T08:46:07Z","cross_cats_sorted":["math-ph","math.FA","math.MP","math.SP"],"title_canon_sha256":"af86569e5eec77bfdfae9b1a275cda004f3c8d0d098f18dc3b57ad219a496e74","abstract_canon_sha256":"dce8750387bbefe0af57bebf0ac53971ba0b18675c3d971840d34e1a1ee741da"},"schema_version":"1.0"},"canonical_sha256":"dadc133e161cfa05c0cb08e7d5caebb2ef9ebee1df45bc6c7877bb68aa523baa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:48.537591Z","signature_b64":"6SMnP7XsAwJDJjtojrAPVVs1YZ4eV8cusrbwafqULdQ4UeXcRKjaSjAGbd7XGlUGHQQ2fu3S/1N+FgEemVa+Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dadc133e161cfa05c0cb08e7d5caebb2ef9ebee1df45bc6c7877bb68aa523baa","last_reissued_at":"2026-05-17T23:43:48.536958Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:48.536958Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1906.03419","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":"2026-05-17T23:43:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"juX7CsXVatTeWY1RBUOL57qLFZSxRIasOOYbpAdKWqxOBIRfvqh7r9Q0l4l8UxZjN3kuJco91mwloc5RUD+tAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T07:50:38.881799Z"},"content_sha256":"586ecad606b6108bae68a8959c26578d5e88002fa376f0799c1ddda7f3428c7d","schema_version":"1.0","event_id":"sha256:586ecad606b6108bae68a8959c26578d5e88002fa376f0799c1ddda7f3428c7d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:3LOBGPQWDT5ALQGLBDT5LSXLWL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lifschitz tail for alloy-type models driven by the fractional Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.FA","math.MP","math.SP"],"primary_cat":"math.PR","authors_text":"Kamil Kaleta, Katarzyna Pietruska-Pa{\\l}uba","submitted_at":"2019-06-08T08:46:07Z","abstract_excerpt":"We establish precise asymptotics near zero of the integrated density of states for the random Schr\\\"{o}dinger operators $(-\\Delta)^{\\alpha/2} + V^{\\omega}$ in $L^2(\\mathbb R^d)$ for the full range of $\\alpha\\in(0,2]$ and a fairly large class of random nonnegative alloy-type potentials $V^{\\omega}$. The IDS exhibits the Lifschitz tail singularity. We prove the existence of the limit $$\\lim_{s\\to 0} s^{d/\\alpha}\\ln\\ell([0,s]) = -C \\left(\\lambda_d^{(\\alpha)}\\right)^{d/\\alpha},$$ with $C \\in (0,\\infty]$. The constant $C$ is is finite if and only if the common distribution of the lattice random var"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.03419","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":""},"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":"2026-05-17T23:43:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U+sXtGplo22C82pAcOu1u9WHou6lna97WP95vxrDNJiI/6WWwiAUI5NxMdKuJWcCPmCbr15dwkAn5BDBmSIQAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T07:50:38.882445Z"},"content_sha256":"217d1d95a1f383de9334e1ee34c3fe9280a565a64d091d33b8a60b12dbcb27b9","schema_version":"1.0","event_id":"sha256:217d1d95a1f383de9334e1ee34c3fe9280a565a64d091d33b8a60b12dbcb27b9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3LOBGPQWDT5ALQGLBDT5LSXLWL/bundle.json","state_url":"https://pith.science/pith/3LOBGPQWDT5ALQGLBDT5LSXLWL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3LOBGPQWDT5ALQGLBDT5LSXLWL/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":"2026-05-27T07:50:38Z","links":{"resolver":"https://pith.science/pith/3LOBGPQWDT5ALQGLBDT5LSXLWL","bundle":"https://pith.science/pith/3LOBGPQWDT5ALQGLBDT5LSXLWL/bundle.json","state":"https://pith.science/pith/3LOBGPQWDT5ALQGLBDT5LSXLWL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3LOBGPQWDT5ALQGLBDT5LSXLWL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:3LOBGPQWDT5ALQGLBDT5LSXLWL","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":"dce8750387bbefe0af57bebf0ac53971ba0b18675c3d971840d34e1a1ee741da","cross_cats_sorted":["math-ph","math.FA","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-06-08T08:46:07Z","title_canon_sha256":"af86569e5eec77bfdfae9b1a275cda004f3c8d0d098f18dc3b57ad219a496e74"},"schema_version":"1.0","source":{"id":"1906.03419","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.03419","created_at":"2026-05-17T23:43:48Z"},{"alias_kind":"arxiv_version","alias_value":"1906.03419v1","created_at":"2026-05-17T23:43:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.03419","created_at":"2026-05-17T23:43:48Z"},{"alias_kind":"pith_short_12","alias_value":"3LOBGPQWDT5A","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"3LOBGPQWDT5ALQGL","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"3LOBGPQW","created_at":"2026-05-18T12:33:07Z"}],"graph_snapshots":[{"event_id":"sha256:217d1d95a1f383de9334e1ee34c3fe9280a565a64d091d33b8a60b12dbcb27b9","target":"graph","created_at":"2026-05-17T23:43:48Z","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 establish precise asymptotics near zero of the integrated density of states for the random Schr\\\"{o}dinger operators $(-\\Delta)^{\\alpha/2} + V^{\\omega}$ in $L^2(\\mathbb R^d)$ for the full range of $\\alpha\\in(0,2]$ and a fairly large class of random nonnegative alloy-type potentials $V^{\\omega}$. The IDS exhibits the Lifschitz tail singularity. We prove the existence of the limit $$\\lim_{s\\to 0} s^{d/\\alpha}\\ln\\ell([0,s]) = -C \\left(\\lambda_d^{(\\alpha)}\\right)^{d/\\alpha},$$ with $C \\in (0,\\infty]$. The constant $C$ is is finite if and only if the common distribution of the lattice random var","authors_text":"Kamil Kaleta, Katarzyna Pietruska-Pa{\\l}uba","cross_cats":["math-ph","math.FA","math.MP","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-06-08T08:46:07Z","title":"Lifschitz tail for alloy-type models driven by the fractional Laplacian"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.03419","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":"sha256:586ecad606b6108bae68a8959c26578d5e88002fa376f0799c1ddda7f3428c7d","target":"record","created_at":"2026-05-17T23:43:48Z","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":"dce8750387bbefe0af57bebf0ac53971ba0b18675c3d971840d34e1a1ee741da","cross_cats_sorted":["math-ph","math.FA","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-06-08T08:46:07Z","title_canon_sha256":"af86569e5eec77bfdfae9b1a275cda004f3c8d0d098f18dc3b57ad219a496e74"},"schema_version":"1.0","source":{"id":"1906.03419","kind":"arxiv","version":1}},"canonical_sha256":"dadc133e161cfa05c0cb08e7d5caebb2ef9ebee1df45bc6c7877bb68aa523baa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dadc133e161cfa05c0cb08e7d5caebb2ef9ebee1df45bc6c7877bb68aa523baa","first_computed_at":"2026-05-17T23:43:48.536958Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:48.536958Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6SMnP7XsAwJDJjtojrAPVVs1YZ4eV8cusrbwafqULdQ4UeXcRKjaSjAGbd7XGlUGHQQ2fu3S/1N+FgEemVa+Bw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:48.537591Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.03419","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:586ecad606b6108bae68a8959c26578d5e88002fa376f0799c1ddda7f3428c7d","sha256:217d1d95a1f383de9334e1ee34c3fe9280a565a64d091d33b8a60b12dbcb27b9"],"state_sha256":"d3545e72e59244584b0ec95d805d1e20dbe0ac5950a0f28707c8b7510da4f576"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"agYf1GsdaZCqs4cXD2m2M8WBdYv/rJBtgKDK+V3JexSWV76YOQtLY0n+/lTZK6gCz2VKKIcjI8f/fekiV8G6BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T07:50:38.885308Z","bundle_sha256":"97e1b01d6aa1dbe1319fed7ad15022919a6a3e07b501b5131fdd3b564d2d8f16"}}