Pith Number

pith:PO4ZL3TO

pith:2007:PO4ZL3TOS34GPUEA6IXTXOACWD

not attested not anchored not stored refs pending

On some new congruences for binomial coefficients

Roberto Tauraso, Zhi-Wei Sun

arxiv:0709.1665 v10 · 2007-09-11 · math.NT · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PO4ZL3TOS34GPUEA6IXTXOACWD}

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	2026-05-18T04:20:51.468736Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7bb995ee6e96f867d080f22f3bb802b0cb8f5cc5b56b7a1b83cb9e466231c26e

Aliases

arxiv: 0709.1665 · arxiv_version: 0709.1665v10 · doi: 10.48550/arxiv.0709.1665 · pith_short_12: PO4ZL3TOS34G · pith_short_16: PO4ZL3TOS34GPUEA · pith_short_8: PO4ZL3TO

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/PO4ZL3TOS34GPUEA6IXTXOACWD \
  | 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: 7bb995ee6e96f867d080f22f3bb802b0cb8f5cc5b56b7a1b83cb9e466231c26e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "570a6c102b86401626f2e6ddd28d83c8fc21de80dac603642dcb4142f646c822",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2007-09-11T17:22:26Z",
    "title_canon_sha256": "ff2bb0c810b3848adef5153a3c4aa55ea992104c8b36d696fd1d2ed6982be124"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0709.1665",
    "kind": "arxiv",
    "version": 10
  }
}