Pith Number

pith:ATQDIX4E

pith:2015:ATQDIX4EGC22FAHX3MLBOXCGEJ

not attested not anchored not stored refs pending

On Abstract $\mathrm{grad}-\mathrm{div}$ Systems

Marcus Waurick, Rainer Picard, Sascha Trostorff, Stefan Seidler

arxiv:1504.02456 v1 · 2015-04-08 · math.AP · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ATQDIX4EGC22FAHX3MLBOXCGEJ}

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	2026-05-18T01:01:16.126561Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

04e0345f8430b5a280f7db16175c46227d530b39c6108cf29dae440d7e6b32c2

Aliases

arxiv: 1504.02456 · arxiv_version: 1504.02456v1 · doi: 10.48550/arxiv.1504.02456 · pith_short_12: ATQDIX4EGC22 · pith_short_16: ATQDIX4EGC22FAHX · pith_short_8: ATQDIX4E

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/ATQDIX4EGC22FAHX3MLBOXCGEJ \
  | 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: 04e0345f8430b5a280f7db16175c46227d530b39c6108cf29dae440d7e6b32c2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e0eca30a5478213d2b5578a6dcfa2a3a0be22c7347c3df2d1082a12b8b0be7d7",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-04-08T14:52:01Z",
    "title_canon_sha256": "65d6d07b3c19ecb8f59111294261383474a282efd9a09a24ba7384e19e30489f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.02456",
    "kind": "arxiv",
    "version": 1
  }
}