Pith Number

pith:YWS4R7XC

pith:2025:YWS4R7XCBPJ5DJZGFZKHJLMJP5

not attested not anchored not stored refs pending

A new proof of Chen's theorem for Markoff graphs

Daniel E. Martin

arxiv:2502.15960 v1 · 2025-02-21 · 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{YWS4R7XCBPJ5DJZGFZKHJLMJP5}

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.

Cited by

1 paper in Pith

Density of integral points in the Betti moduli of quasi-projective varieties

Receipt and verification

First computed	2026-07-05T10:18:19.095947Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c5a5c8fee20bd3d1a7262e5474ad897f6666bea8dfa4432812ffb519f982ce4e

Aliases

arxiv: 2502.15960 · arxiv_version: 2502.15960v1 · doi: 10.48550/arxiv.2502.15960 · pith_short_12: YWS4R7XCBPJ5 · pith_short_16: YWS4R7XCBPJ5DJZG · pith_short_8: YWS4R7XC

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/YWS4R7XCBPJ5DJZGFZKHJLMJP5 \
  | 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: c5a5c8fee20bd3d1a7262e5474ad897f6666bea8dfa4432812ffb519f982ce4e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3afaed39f7f5c70c72e1c16205c5dcb691509c7245e3dd4175cf638aeb7d9107",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2025-02-21T21:44:36Z",
    "title_canon_sha256": "a6444f8e2de15d992ef69b5885f3d7bd03ce064fba6e6fc90b454487be9fe849"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2502.15960",
    "kind": "arxiv",
    "version": 1
  }
}