Pith Number

pith:X7XEIKVB

pith:2012:X7XEIKVB2UY7CUXNOV3BTEAOZH

not attested not anchored not stored refs pending

Relative Critical Points

Debra Lewis

arxiv:1210.0278 v2 · 2012-10-01 · math.DS · math.SG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{X7XEIKVB2UY7CUXNOV3BTEAOZH}

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	2026-05-18T03:25:33.331540Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bfee442aa1d531f152ed757619900ec9ec7043ba285a32919a941a76841f6a51

Aliases

arxiv: 1210.0278 · arxiv_version: 1210.0278v2 · doi: 10.48550/arxiv.1210.0278 · pith_short_12: X7XEIKVB2UY7 · pith_short_16: X7XEIKVB2UY7CUXN · pith_short_8: X7XEIKVB

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/X7XEIKVB2UY7CUXNOV3BTEAOZH \
  | 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: bfee442aa1d531f152ed757619900ec9ec7043ba285a32919a941a76841f6a51

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bbf66ca9080651b44010dc74a0d253a33fd54eb0784afb753b503e6782ac9296",
    "cross_cats_sorted": [
      "math.SG"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/3.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-10-01T03:10:02Z",
    "title_canon_sha256": "5b73893776fdd18502466ff56091cf9651c5844e14fc19ad0af8485fceb14cdd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.0278",
    "kind": "arxiv",
    "version": 2
  }
}