Pith Number

pith:K4GQXO27

pith:2016:K4GQXO27HG5IZEWYFT3UTOM3OG

not attested not anchored not stored refs pending

Rational and Polynomial Density on Compact Real Manifolds

Purvi Gupta, Rasul Shafikov

arxiv:1602.05872 v4 · 2016-02-18 · math.CV · math.SG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{K4GQXO27HG5IZEWYFT3UTOM3OG}

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	2026-05-18T01:11:57.654640Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

570d0bbb5f39ba8c92d82cf749b99b718d6dea3c1cc9f8936b8964a158b4a27c

Aliases

arxiv: 1602.05872 · arxiv_version: 1602.05872v4 · doi: 10.48550/arxiv.1602.05872 · pith_short_12: K4GQXO27HG5I · pith_short_16: K4GQXO27HG5IZEWY · pith_short_8: K4GQXO27

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/K4GQXO27HG5IZEWYFT3UTOM3OG \
  | 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: 570d0bbb5f39ba8c92d82cf749b99b718d6dea3c1cc9f8936b8964a158b4a27c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5c348ceb74b4ccc602671e83e79b4c338c443d64ea0595dd5dbf0044313f3345",
    "cross_cats_sorted": [
      "math.SG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2016-02-18T16:48:32Z",
    "title_canon_sha256": "a067020f85185b3b9bce1b77210dc19b4dfe05197c508ba85459f4fba24e6c64"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1602.05872",
    "kind": "arxiv",
    "version": 4
  }
}