Pith Number

pith:P4ZRU2FU

pith:2016:P4ZRU2FUTO6G7L4NSHPU3U6PKT

not attested not anchored not stored refs pending

An Improved Fountain Theorem and its Application

Huan-Song Zhou, Long-Jiang Gu

arxiv:1612.05392 v1 · 2016-12-16 · 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{P4ZRU2FUTO6G7L4NSHPU3U6PKT}

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	2026-05-18T00:54:51.891341Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7f331a68b49bbc6faf8d91df4dd3cf54e8dd1ec8259c28ae2ad1e8f796ecd18e

Aliases

arxiv: 1612.05392 · arxiv_version: 1612.05392v1 · doi: 10.48550/arxiv.1612.05392 · pith_short_12: P4ZRU2FUTO6G · pith_short_16: P4ZRU2FUTO6G7L4N · pith_short_8: P4ZRU2FU

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/P4ZRU2FUTO6G7L4NSHPU3U6PKT \
  | 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: 7f331a68b49bbc6faf8d91df4dd3cf54e8dd1ec8259c28ae2ad1e8f796ecd18e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dc72a7dcef347304faaae58133accaf0ef75925de8fb868ba47051c69b4238d7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2016-12-16T08:23:47Z",
    "title_canon_sha256": "287054287877d744b52d991bbcb418eac0c7f8c95f038d83e778c161092e6fe8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.05392",
    "kind": "arxiv",
    "version": 1
  }
}