Pith Number

pith:2LJ5GWZ2

pith:2010:2LJ5GWZ2II2NFJCWZD6XAD5CVZ

not attested not anchored not stored refs pending

A simple proof of the Fredholm Alternative

Otgonbayar Uuye

arxiv:1011.2933 v1 · 2010-11-12 · 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{2LJ5GWZ2II2NFJCWZD6XAD5CVZ}

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	2026-05-18T04:36:07.796512Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d2d3d35b3a4234d2a456c8fd700fa2ae4fac08b8379099eb7e0e3c332ac94eac

Aliases

arxiv: 1011.2933 · arxiv_version: 1011.2933v1 · doi: 10.48550/arxiv.1011.2933 · pith_short_12: 2LJ5GWZ2II2N · pith_short_16: 2LJ5GWZ2II2NFJCW · pith_short_8: 2LJ5GWZ2

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/2LJ5GWZ2II2NFJCWZD6XAD5CVZ \
  | 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: d2d3d35b3a4234d2a456c8fd700fa2ae4fac08b8379099eb7e0e3c332ac94eac

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "56fda44fdd29bf7d445d1d173e1e95702bb555f55d51e6b3393bc7375f0ffd29",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2010-11-12T14:59:03Z",
    "title_canon_sha256": "b58851367dd13953c40987a1ab53dea0e6e5d10b7633b4a32207bea3c7e75bf9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.2933",
    "kind": "arxiv",
    "version": 1
  }
}