Pith Number

pith:DZKRA67B

pith:2011:DZKRA67B2ILTFCELHNFSQYRVBF

not attested not anchored not stored refs pending

Mark Krein's Method of Directing Functionals and Singular Potentials

Annemarie Luger, Charles Fulton, Heinz Langer

arxiv:1110.6709 v1 · 2011-10-31 · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DZKRA67B2ILTFCELHNFSQYRVBF}

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	2026-05-18T04:09:54.324938Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1e55107be1d21732888b3b4b2862350951880fe1cf9ffbfb9ce6a08fe4563079

Aliases

arxiv: 1110.6709 · arxiv_version: 1110.6709v1 · doi: 10.48550/arxiv.1110.6709 · pith_short_12: DZKRA67B2ILT · pith_short_16: DZKRA67B2ILTFCEL · pith_short_8: DZKRA67B

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/DZKRA67B2ILTFCELHNFSQYRVBF \
  | 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: 1e55107be1d21732888b3b4b2862350951880fe1cf9ffbfb9ce6a08fe4563079

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3502f3067b64f0a53730f199792dcc89689dd2a22e197462ac8ab42b1174e88c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2011-10-31T07:51:37Z",
    "title_canon_sha256": "1c97804abedb0428aaa932dd6a7860979b1a1f5ebeb446035d578cf6373e7c75"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.6709",
    "kind": "arxiv",
    "version": 1
  }
}