Pith Number

pith:7HREZH2C

pith:2012:7HREZH2C3UPILQQXTKJWGHNHW5

not attested not anchored not stored refs pending

Convexity of reduced energy and mass angular momentum inequalities

Richard Schoen, Xin Zhou

arxiv:1209.0019 v1 · 2012-08-31 · math.DG · gr-qc

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7HREZH2C3UPILQQXTKJWGHNHW5}

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	2026-05-18T01:54:48.788916Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f9e24c9f42dd1e85c2179a93631da7b776b9ac8c381214dbcc5ec170223e3429

Aliases

arxiv: 1209.0019 · arxiv_version: 1209.0019v1 · doi: 10.48550/arxiv.1209.0019 · pith_short_12: 7HREZH2C3UPI · pith_short_16: 7HREZH2C3UPILQQX · pith_short_8: 7HREZH2C

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/7HREZH2C3UPILQQXTKJWGHNHW5 \
  | 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: f9e24c9f42dd1e85c2179a93631da7b776b9ac8c381214dbcc5ec170223e3429

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2f20368ebd43b6fca49cd3217bc0ab730556b5af3e33183f594684131da9c4f4",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2012-08-31T21:24:58Z",
    "title_canon_sha256": "eea3cf0d3c2ec03698ea98020229a60d15d2338c3569ff54bcc402e6c8aac014"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.0019",
    "kind": "arxiv",
    "version": 1
  }
}