Pith Number

pith:ABZD2IH5

pith:2019:ABZD2IH5MKWP6UJSUCVIESXSPD

not attested not anchored not stored refs pending

A remark on convergence almost-everywhere of eigenfunction expansions of elliptic operators

Ravshan Ashurov

arxiv:1902.02035 v2 · 2019-02-06 · math.AP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ABZD2IH5MKWP6UJSUCVIESXSPD}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-17T23:51:55.694690Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

00723d20fd62acff5132a0aa824af278e75aeb05ad8ce63201e2d16db924abe2

Aliases

arxiv: 1902.02035 · arxiv_version: 1902.02035v2 · doi: 10.48550/arxiv.1902.02035 · pith_short_12: ABZD2IH5MKWP · pith_short_16: ABZD2IH5MKWP6UJS · pith_short_8: ABZD2IH5

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/ABZD2IH5MKWP6UJSUCVIESXSPD \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 00723d20fd62acff5132a0aa824af278e75aeb05ad8ce63201e2d16db924abe2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a6e90bf440f20d0262b89a39510b2f57f998da62161e25ee47263e26d4e53799",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2019-02-06T06:06:14Z",
    "title_canon_sha256": "50d3ee8574d0dccc73dec00178daa7a12d81d5c0d84cc40171ea90f2dd6b2614"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1902.02035",
    "kind": "arxiv",
    "version": 2
  }
}