Pith Number

pith:XTDGQFTF

pith:2012:XTDGQFTFFAFQGBXSPRHWNOVIQY

not attested not anchored not stored refs pending

Improvement of eigenfunction estimates on manifolds of nonpositive curvature

Andrew Hassell, Melissa Tacy

arxiv:1212.2540 v2 · 2012-12-11 · math.AP · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XTDGQFTFFAFQGBXSPRHWNOVIQY}

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	2026-05-18T01:22:49.176799Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bcc6681665280b0306f27c4f66baa8860bb2c20fef7eddec5c5dc8124bd109e4

Aliases

arxiv: 1212.2540 · arxiv_version: 1212.2540v2 · doi: 10.48550/arxiv.1212.2540 · pith_short_12: XTDGQFTFFAFQ · pith_short_16: XTDGQFTFFAFQGBXS · pith_short_8: XTDGQFTF

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/XTDGQFTFFAFQGBXSPRHWNOVIQY \
  | 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: bcc6681665280b0306f27c4f66baa8860bb2c20fef7eddec5c5dc8124bd109e4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e3ae228f5d351f07aedd0c71e5842717fee82bd07186009d5b650e9dbf92cd55",
    "cross_cats_sorted": [
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-12-11T17:06:30Z",
    "title_canon_sha256": "84a6fd321eb4398f37a55fccc6aef50e9b889233205ca28a356c6fcb8f75113e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.2540",
    "kind": "arxiv",
    "version": 2
  }
}