Pith Number

pith:NKQDCWBJ

pith:2015:NKQDCWBJUBYOHHWS2BQN4MZ36B

not attested not anchored not stored refs pending

Note on a theorem of Bangert

Tian-Jun Li, WeiWei Wu

arxiv:1509.08128 v1 · 2015-09-27 · math.SG · math.CV

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NKQDCWBJUBYOHHWS2BQN4MZ36B}

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	2026-05-18T01:31:54.655043Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6aa0315829a070e39ed2d060de333bf0653ea269932fd9f79cd11eccdba575c9

Aliases

arxiv: 1509.08128 · arxiv_version: 1509.08128v1 · doi: 10.48550/arxiv.1509.08128 · pith_short_12: NKQDCWBJUBYO · pith_short_16: NKQDCWBJUBYOHHWS · pith_short_8: NKQDCWBJ

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/NKQDCWBJUBYOHHWS2BQN4MZ36B \
  | 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: 6aa0315829a070e39ed2d060de333bf0653ea269932fd9f79cd11eccdba575c9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dca783b85438d4b40ed4245c7a11c5b0cf139c804bc934b0ff43fffaa4473fe8",
    "cross_cats_sorted": [
      "math.CV"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SG",
    "submitted_at": "2015-09-27T19:38:14Z",
    "title_canon_sha256": "b72de3258f673430d9d0c8295ac28be9b6a3d814c9c01875ef4eb311e175c97c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.08128",
    "kind": "arxiv",
    "version": 1
  }
}