Pith Number

pith:HHIJURCU

pith:2018:HHIJURCUZSYDET3F7AZ3CRE4LM

not attested not anchored not stored refs pending

Combinatorial proofs of the Newton-Girard and Chapman-Costas-Santos identities

Sajal Kumar Mukherjee, Sudip Bera

arxiv:1807.11749 v2 · 2018-07-31 · 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{HHIJURCUZSYDET3F7AZ3CRE4LM}

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	2026-05-18T00:03:45.938626Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

39d09a4454ccb0324f65f833b1449c5b1df4452f8b19aa1b07f28094d357dd87

Aliases

arxiv: 1807.11749 · arxiv_version: 1807.11749v2 · doi: 10.48550/arxiv.1807.11749 · pith_short_12: HHIJURCUZSYD · pith_short_16: HHIJURCUZSYDET3F · pith_short_8: HHIJURCU

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/HHIJURCUZSYDET3F7AZ3CRE4LM \
  | 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: 39d09a4454ccb0324f65f833b1449c5b1df4452f8b19aa1b07f28094d357dd87

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e7a7a8734c7010d09251795c26278dc74dace4dfec13508d928969a4a594882b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-07-31T10:45:29Z",
    "title_canon_sha256": "24740f47d09f5a17196b9b915d7e921a2700472ee2a2f32fc1020a6378e66e37"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1807.11749",
    "kind": "arxiv",
    "version": 2
  }
}