Pith Number

pith:4OHEJIQR

pith:2017:4OHEJIQRHLP5JSBQDBD2HX2OTB

not attested not anchored not stored refs pending

Popular progression differences in vector spaces

Huy Tuan Pham, Jacob Fox

arxiv:1708.08482 v1 · 2017-08-28 · math.CO · 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{4OHEJIQRHLP5JSBQDBD2HX2OTB}

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	2026-05-18T00:36:27.614700Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e38e44a2113adfd4c8301847a3df4e985a81532c72932364d181d7585810bed7

Aliases

arxiv: 1708.08482 · arxiv_version: 1708.08482v1 · doi: 10.48550/arxiv.1708.08482 · pith_short_12: 4OHEJIQRHLP5 · pith_short_16: 4OHEJIQRHLP5JSBQ · pith_short_8: 4OHEJIQR

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/4OHEJIQRHLP5JSBQDBD2HX2OTB \
  | 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: e38e44a2113adfd4c8301847a3df4e985a81532c72932364d181d7585810bed7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d8c52bf015138dabbbac2345e9cc0079a7f99722e52973f33613c7d19f2c665b",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2017-08-28T18:55:08Z",
    "title_canon_sha256": "7c7737397243fbc1483e02f1ff35aa1e0924558b363cbb2b62f486ce900a2796"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1708.08482",
    "kind": "arxiv",
    "version": 1
  }
}