Pith Number

pith:GCEKJ2N3

pith:2010:GCEKJ2N3UZFG5MWGOXFANWAWT5

not attested not anchored not stored refs pending

Moebius Schrodinger

Jean Bourgain

arxiv:1012.5217 v1 · 2010-12-23 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GCEKJ2N3UZFG5MWGOXFANWAWT5}

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	2026-05-18T04:32:35.567585Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3088a4e9bba64a6eb2c675ca06d8169f69e1beadc4d2ca6fe433237ed51a8f1c

Aliases

arxiv: 1012.5217 · arxiv_version: 1012.5217v1 · doi: 10.48550/arxiv.1012.5217 · pith_short_12: GCEKJ2N3UZFG · pith_short_16: GCEKJ2N3UZFG5MWG · pith_short_8: GCEKJ2N3

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/GCEKJ2N3UZFG5MWGOXFANWAWT5 \
  | 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: 3088a4e9bba64a6eb2c675ca06d8169f69e1beadc4d2ca6fe433237ed51a8f1c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1f5ebc1add2c010f6955c677819dd7cf8511c15d30f12722ff0cbf19636f9a69",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2010-12-23T14:36:23Z",
    "title_canon_sha256": "8b3faefd89f731db2a378a0727fa931c3bf8f0d3a413a603290bf05a20dab7c8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.5217",
    "kind": "arxiv",
    "version": 1
  }
}