Pith Number

pith:TFIL2EWI

pith:2016:TFIL2EWIIY2EJXZLM7RXBNJSGC

not attested not anchored not stored refs pending

On alternating sums of binomial coefficients and $q$-binomial coefficients

Mohamed El Bachraoui

arxiv:1603.03881 v2 · 2016-03-12 · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TFIL2EWIIY2EJXZLM7RXBNJSGC}

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	2026-05-18T01:12:54.885441Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9950bd12c8463444df2b67e370b5323091453d1066541f24959689457c47249e

Aliases

arxiv: 1603.03881 · arxiv_version: 1603.03881v2 · doi: 10.48550/arxiv.1603.03881 · pith_short_12: TFIL2EWIIY2E · pith_short_16: TFIL2EWIIY2EJXZL · pith_short_8: TFIL2EWI

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/TFIL2EWIIY2EJXZLM7RXBNJSGC \
  | 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: 9950bd12c8463444df2b67e370b5323091453d1066541f24959689457c47249e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a48543da8164049abf6bfe1c4671dcffce41d51d462189e694a5add778563a7a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-03-12T09:40:38Z",
    "title_canon_sha256": "7dcd68d006352fe9b991d7421f71c1b9155906229c2bc354e96c9510ce0f715d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.03881",
    "kind": "arxiv",
    "version": 2
  }
}