Pith Number

pith:NGUOUV36

pith:2026:NGUOUV367QEDMIYIP5MAWWGKCY

not attested not anchored not stored refs pending

Explicit formulas for gradients and the divergence in n-dimensional spherical coordinates

Bern Rummler, Gudrun Th\"ater

arxiv:2607.01096 v1 · 2026-07-01 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NGUOUV367QEDMIYIP5MAWWGKCY}

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	2026-07-02T01:18:28.926965Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

69a8ea577efc083623087f580b58ca1619d7a4c838a4b1c0bb7f7efad20b740b

Aliases

arxiv: 2607.01096 · arxiv_version: 2607.01096v1 · doi: 10.48550/arxiv.2607.01096 · pith_short_12: NGUOUV367QED · pith_short_16: NGUOUV367QEDMIYI · pith_short_8: NGUOUV36

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/NGUOUV367QEDMIYIP5MAWWGKCY \
  | 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: 69a8ea577efc083623087f580b58ca1619d7a4c838a4b1c0bb7f7efad20b740b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "38faa5574e83545871d8db35c01af2fbb46aa9923c82e9548ddf7467e79f6210",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-07-01T15:49:42Z",
    "title_canon_sha256": "79cb7bb0616ed87178d36bfdc66a615866b4c8d498aa4e886cbae1afa4025b5d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.01096",
    "kind": "arxiv",
    "version": 1
  }
}