Pith Number

pith:GYXL7G3K

pith:2011:GYXL7G3KEM6DFEGRSB4KKEXKFR

not attested not anchored not stored refs pending

Continuous symmetrization via polarization

Alexander Yu. Solynin

arxiv:1102.1004 v1 · 2011-02-04 · 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{GYXL7G3KEM6DFEGRSB4KKEXKFR}

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	2026-05-18T04:30:03.266002Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

362ebf9b6a233c3290d19078a512ea2c512152518f457faafcc3602e1748a298

Aliases

arxiv: 1102.1004 · arxiv_version: 1102.1004v1 · doi: 10.48550/arxiv.1102.1004 · pith_short_12: GYXL7G3KEM6D · pith_short_16: GYXL7G3KEM6DFEGR · pith_short_8: GYXL7G3K

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/GYXL7G3KEM6DFEGRSB4KKEXKFR \
  | 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: 362ebf9b6a233c3290d19078a512ea2c512152518f457faafcc3602e1748a298

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "72b03aaadf4a9f5949b527ee4cd5a08721446133e48034e55f5814ddccb13c7b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-02-04T19:48:22Z",
    "title_canon_sha256": "8a14d108e583b9e67fc503708f14773ccb2e3ad91cab27b8adc99741b277c006"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.1004",
    "kind": "arxiv",
    "version": 1
  }
}