Pith Number

pith:Q3DEY5O4

pith:2014:Q3DEY5O4FDHXUI5QSQXYLLOE2G

not attested not anchored not stored refs pending

Order-preserving Freiman isomorphisms

Albert Bush, Ernie Croot, Gagik Amirkhanyan

arxiv:1409.8535 v2 · 2014-09-30 · 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{Q3DEY5O4FDHXUI5QSQXYLLOE2G}

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	2026-05-18T00:56:46.927791Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

86c64c75dc28cf7a23b0942f85adc4d1a58ad67505ddb43b76351118f1ded135

Aliases

arxiv: 1409.8535 · arxiv_version: 1409.8535v2 · doi: 10.48550/arxiv.1409.8535 · pith_short_12: Q3DEY5O4FDHX · pith_short_16: Q3DEY5O4FDHXUI5Q · pith_short_8: Q3DEY5O4

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/Q3DEY5O4FDHXUI5QSQXYLLOE2G \
  | 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: 86c64c75dc28cf7a23b0942f85adc4d1a58ad67505ddb43b76351118f1ded135

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4cf83bfec407a175d57d4b24a4b84b0a512d0c5963a517d6d744ebf3da6376a0",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2014-09-30T13:16:44Z",
    "title_canon_sha256": "4a0d55a2eafad6df4d085358c10f4b1946721f17213ee33fa958a028b9298206"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1409.8535",
    "kind": "arxiv",
    "version": 2
  }
}