Pith Number

pith:C4AUHYIJ

pith:2015:C4AUHYIJMQZTMDU6PIIAZ3VO5Y

not attested not anchored not stored refs pending

On Stability of Nodal $L_k^p$-Maps I

Gang Liu

arxiv:1509.07187 v2 · 2015-09-24 · math.SG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{C4AUHYIJMQZTMDU6PIIAZ3VO5Y}

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	2026-05-17T23:44:43.724555Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

170143e1096433360e9e7a100ceeaeee0aa8cb8537342c25cb1738afbff02b1e

Aliases

arxiv: 1509.07187 · arxiv_version: 1509.07187v2 · doi: 10.48550/arxiv.1509.07187 · pith_short_12: C4AUHYIJMQZT · pith_short_16: C4AUHYIJMQZTMDU6 · pith_short_8: C4AUHYIJ

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/C4AUHYIJMQZTMDU6PIIAZ3VO5Y \
  | 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: 170143e1096433360e9e7a100ceeaeee0aa8cb8537342c25cb1738afbff02b1e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "36dabe967eaf7c2cafb8831b04e04199f3afcac2c4c1ed50d724d7a4460f4537",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SG",
    "submitted_at": "2015-09-24T00:21:08Z",
    "title_canon_sha256": "62be9d43c33ad7cde15de480673b0ccacd9658da14a66764097eedaed03d2781"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.07187",
    "kind": "arxiv",
    "version": 2
  }
}