Pith Number

pith:IFQ2DL23

pith:2015:IFQ2DL23VXBC45J7JLHQUPJVEE

not attested not anchored not stored refs pending

The trace as an average over the unit sphere of a normed space with a 1-symmetric basis

Kent E. Morrison, Tomasz Kania

arxiv:1511.02084 v1 · 2015-11-06 · math.FA · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IFQ2DL23VXBC45J7JLHQUPJVEE}

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	2026-05-18T01:00:10.018203Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4161a1af5badc22e753f4acf0a3d35210bbe721ed17adabc124f150b9a091c8d

Aliases

arxiv: 1511.02084 · arxiv_version: 1511.02084v1 · doi: 10.48550/arxiv.1511.02084 · pith_short_12: IFQ2DL23VXBC · pith_short_16: IFQ2DL23VXBC45J7 · pith_short_8: IFQ2DL23

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/IFQ2DL23VXBC45J7JLHQUPJVEE \
  | 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: 4161a1af5badc22e753f4acf0a3d35210bbe721ed17adabc124f150b9a091c8d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c807fa50ec82d3ff3abeee3dd8baaf956da4806dab16073edbbc820198a08307",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2015-11-06T14:10:05Z",
    "title_canon_sha256": "80d69d609bfaf503c5236c562bd2daef38e7a580c59fb1ac09cb5d44a857d554"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.02084",
    "kind": "arxiv",
    "version": 1
  }
}