Pith Number

pith:GSKXIFCG

pith:2012:GSKXIFCGZWPUU3I2YIHKKKDKDQ

not attested not anchored not stored refs pending

Deformations and Hilbert's Fourth Problem

Changtao Yu

arxiv:1209.0845 v1 · 2012-09-05 · math.DG · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GSKXIFCGZWPUU3I2YIHKKKDKDQ}

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	2026-05-18T03:25:35.037018Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3495741446cd9f4a6d1ac20ea5286a1c18358024f5cbf81b57556a0555224ee9

Aliases

arxiv: 1209.0845 · arxiv_version: 1209.0845v1 · doi: 10.48550/arxiv.1209.0845 · pith_short_12: GSKXIFCGZWPU · pith_short_16: GSKXIFCGZWPUU3I2 · pith_short_8: GSKXIFCG

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/GSKXIFCGZWPUU3I2YIHKKKDKDQ \
  | 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: 3495741446cd9f4a6d1ac20ea5286a1c18358024f5cbf81b57556a0555224ee9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "67119dfc331ca7cbfc88cf1b927c25d5007fdb483b480f893a77450c8dff70a7",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2012-09-05T01:57:40Z",
    "title_canon_sha256": "21771d6a311b3434b2fba353671978b4f57c362b0d8b1cf82bb2c89d64a35380"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.0845",
    "kind": "arxiv",
    "version": 1
  }
}