Pith Number

pith:BA7QAZLM

pith:2018:BA7QAZLMOXWDS34YLGCJLBKMRE

not attested not anchored not stored refs pending

On the Gradient of Harmonic Functions

Pisheng Ding

arxiv:1811.04204 v2 · 2018-11-10 · math.CA · math.AP · 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{BA7QAZLMOXWDS34YLGCJLBKMRE}

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	2026-05-17T23:58:57.050198Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

083f00656c75ec396f98598495854c8935434e23b99e659cd77df21e8e0d8c50

Aliases

arxiv: 1811.04204 · arxiv_version: 1811.04204v2 · doi: 10.48550/arxiv.1811.04204 · pith_short_12: BA7QAZLMOXWD · pith_short_16: BA7QAZLMOXWDS34Y · pith_short_8: BA7QAZLM

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/BA7QAZLMOXWDS34YLGCJLBKMRE \
  | 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: 083f00656c75ec396f98598495854c8935434e23b99e659cd77df21e8e0d8c50

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0ecbff280e5c7889101e48327c6a16f020372889cf99743b419cacec93ace093",
    "cross_cats_sorted": [
      "math.AP",
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2018-11-10T06:49:47Z",
    "title_canon_sha256": "b9ee33b45522ff2e38c4cb07ec4d3f05df94cccf90468541ddf676b106e18e5b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1811.04204",
    "kind": "arxiv",
    "version": 2
  }
}