Pith Number

pith:5MHIL7IG

pith:2010:5MHIL7IGKBL3BKQS3LMCT5TJ3N

not attested not anchored not stored refs pending

Hyperbolic Gradient Flow: Evolution of Graphs in R^{n+1}

De-Xing Kong, Kefeng Liu

arxiv:1009.3993 v1 · 2010-09-21 · math.DG · 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{5MHIL7IGKBL3BKQS3LMCT5TJ3N}

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	2026-05-18T01:04:58.369584Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eb0e85fd065057b0aa12dad829f669db40d0602058e78a0e1a0812c32d0e0680

Aliases

arxiv: 1009.3993 · arxiv_version: 1009.3993v1 · doi: 10.48550/arxiv.1009.3993 · pith_short_12: 5MHIL7IGKBL3 · pith_short_16: 5MHIL7IGKBL3BKQS · pith_short_8: 5MHIL7IG

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/5MHIL7IGKBL3BKQS3LMCT5TJ3N \
  | 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: eb0e85fd065057b0aa12dad829f669db40d0602058e78a0e1a0812c32d0e0680

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cd951621fbd68cb883c38e6399785ec571a066c64ba0b076fe0421eef18032e9",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2010-09-21T03:46:04Z",
    "title_canon_sha256": "485d40265b6bbeb6626d6fe077e3018ab74310fd412af6fc7887a57376139e0f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.3993",
    "kind": "arxiv",
    "version": 1
  }
}