Pith Number

pith:6D3HENPE

pith:2015:6D3HENPEYMXN4Z57DAQT757QDI

not attested not anchored not stored refs pending

Monotonicity formulas for coupled elliptic gradient systems with applications

Henrik Shahgholian, Mostafa Fazly

arxiv:1509.08153 v2 · 2015-09-27 · math.AP · math-ph · math.DG · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6D3HENPEYMXN4Z57DAQT757QDI}

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	2026-05-17T23:56:43.279179Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f0f67235e4c32ede67bf18213ff7f01a39ecbbf9e611a01a0ec7fdcf57410ddf

Aliases

arxiv: 1509.08153 · arxiv_version: 1509.08153v2 · doi: 10.48550/arxiv.1509.08153 · pith_short_12: 6D3HENPEYMXN · pith_short_16: 6D3HENPEYMXN4Z57 · pith_short_8: 6D3HENPE

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/6D3HENPEYMXN4Z57DAQT757QDI \
  | 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: f0f67235e4c32ede67bf18213ff7f01a39ecbbf9e611a01a0ec7fdcf57410ddf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "762acec6ebba23367e59f0d414d523a2e27613d758283576bdfd22a5436f8790",
    "cross_cats_sorted": [
      "math-ph",
      "math.DG",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-09-27T22:09:44Z",
    "title_canon_sha256": "6ae58a7a4bb303f79a3b8a0f2e528c45c05c6139d3f4e78d07c23bd8a0b88a80"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.08153",
    "kind": "arxiv",
    "version": 2
  }
}