Pith Number

pith:2TRJNZ36

pith:2011:2TRJNZ36LMU4WDBGRYYVG73A2E

not attested not anchored not stored refs pending

On the integrality of the elementary symmetric functions of $1, 1/3, ..., 1/(2n-1)$

Chunlin Wang, Shaofang Hong

arxiv:1112.0853 v1 · 2011-12-05 · 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{2TRJNZ36LMU4WDBGRYYVG73A2E}

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	2026-05-18T04:06:57.596532Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d4e296e77e5b29cb0c268e31537f60d12d28060375681da2aabe589f1163c54e

Aliases

arxiv: 1112.0853 · arxiv_version: 1112.0853v1 · doi: 10.48550/arxiv.1112.0853 · pith_short_12: 2TRJNZ36LMU4 · pith_short_16: 2TRJNZ36LMU4WDBG · pith_short_8: 2TRJNZ36

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/2TRJNZ36LMU4WDBGRYYVG73A2E \
  | 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: d4e296e77e5b29cb0c268e31537f60d12d28060375681da2aabe589f1163c54e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a1b1509dfe83aec3844eebf0034f80ff9eb1f1af142d9a9d15df9d0427f278a9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-12-05T07:46:36Z",
    "title_canon_sha256": "25ab2f362f282c373279b608f860d755aa04ef059716419fa4179722496aec9e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.0853",
    "kind": "arxiv",
    "version": 1
  }
}