Pith Number

pith:XBJT6NVM

pith:2004:XBJT6NVM5P2D5ZZDX263XWAWMV

not attested not anchored not stored refs pending

Quasi-symmetric functions and mod p multiple harmonic sums

Michael E. Hoffman

arxiv:math/0401319 v3 · 2004-01-23 · 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{XBJT6NVM5P2D5ZZDX263XWAWMV}

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	2026-05-18T01:03:12.310895Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b8533f36acebf43ee723bebdbbd81665435cbd203ab10a91494598198f5a7ed6

Aliases

arxiv: math/0401319 · arxiv_version: math/0401319v3 · doi: 10.48550/arxiv.math/0401319 · pith_short_12: XBJT6NVM5P2D · pith_short_16: XBJT6NVM5P2D5ZZD · pith_short_8: XBJT6NVM

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/XBJT6NVM5P2D5ZZDX263XWAWMV \
  | 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: b8533f36acebf43ee723bebdbbd81665435cbd203ab10a91494598198f5a7ed6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ae6d498357169b6e5da05ce8f5609b15a54e2165a9459ef0bb81e4045989ee65",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/publicdomain/",
    "primary_cat": "math.NT",
    "submitted_at": "2004-01-23T16:28:20Z",
    "title_canon_sha256": "84ab2c36f2873e89bb3944099c002fb479edb09a3e7ee5ca49fc70311516e22d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0401319",
    "kind": "arxiv",
    "version": 3
  }
}