Pith Number

pith:JL2JQWBZ

pith:2015:JL2JQWBZTLPROMZ3UU6PTB43YM

not attested not anchored not stored refs pending

Concerning Toponogov's Theorem and logarithmic improvement of estimates of eigenfunctions

Christopher D. Sogge, Matthew D. Blair

arxiv:1510.07726 v2 · 2015-10-26 · math.AP · math.CA · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JL2JQWBZTLPROMZ3UU6PTB43YM}

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	2026-05-18T01:28:37.514524Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4af49858399adf17333ba53cf9879bc309c7d11c7eb91f3cecf458668c270853

Aliases

arxiv: 1510.07726 · arxiv_version: 1510.07726v2 · doi: 10.48550/arxiv.1510.07726 · pith_short_12: JL2JQWBZTLPR · pith_short_16: JL2JQWBZTLPROMZ3 · pith_short_8: JL2JQWBZ

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/JL2JQWBZTLPROMZ3UU6PTB43YM \
  | 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: 4af49858399adf17333ba53cf9879bc309c7d11c7eb91f3cecf458668c270853

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9c5e68c37885c1c23aef342a02883bd508ad920c3b6ed52258eea81c2dec0040",
    "cross_cats_sorted": [
      "math.CA",
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-10-26T23:54:56Z",
    "title_canon_sha256": "8f7b22fc357220d18fda0711f1d0f12ec6654ee5bab2c5096f29ee8f203b00e0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.07726",
    "kind": "arxiv",
    "version": 2
  }
}