Pith Number

pith:FXSRY4IH

pith:2005:FXSRY4IH23LAEVL6SD476YXHW4

not attested not anchored not stored refs pending

Mixed sums of squares and triangular numbers (II)

Hao Pan, Song Guo, Zhi-Wei Sun

arxiv:math/0505187 v5 · 2005-05-10 · 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{FXSRY4IH23LAEVL6SD476YXHW4}

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	2026-07-04T15:06:27.041510Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2de51c7107d6d602557e90f9ff62e7b718fdfec28711f6e0f1d4bc3e58f411a2

Aliases

arxiv: math/0505187 · arxiv_version: math/0505187v5 · doi: 10.48550/arxiv.math/0505187 · pith_short_12: FXSRY4IH23LA · pith_short_16: FXSRY4IH23LAEVL6 · pith_short_8: FXSRY4IH

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/FXSRY4IH23LAEVL6SD476YXHW4 \
  | 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: 2de51c7107d6d602557e90f9ff62e7b718fdfec28711f6e0f1d4bc3e58f411a2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1092ebc704587ac79daecda789734120396b742e43d844c17124f92215ac35f9",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2005-05-10T19:16:26Z",
    "title_canon_sha256": "5bd0fab1136c0c43c3fb88f7c27ad78ba20145a1d43b66c50465b254c145b110"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0505187",
    "kind": "arxiv",
    "version": 5
  }
}