Pith Number

pith:W5SFO37W

pith:2018:W5SFO37WYCZGHYELO7N5QXJKMF

not attested not anchored not stored refs pending

Gradient estimates via two-point functions for elliptic equations on manifolds

Ben Andrews, Changwei Xiong

arxiv:1808.09615 v1 · 2018-08-29 · 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{W5SFO37WYCZGHYELO7N5QXJKMF}

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	2026-05-17T23:47:02.903362Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b764576ff6c0b263e08b77dbd85d2a615a9e1d6f6998cfa89db077e18652cb48

Aliases

arxiv: 1808.09615 · arxiv_version: 1808.09615v1 · doi: 10.48550/arxiv.1808.09615 · pith_short_12: W5SFO37WYCZG · pith_short_16: W5SFO37WYCZGHYEL · pith_short_8: W5SFO37W

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/W5SFO37WYCZGHYELO7N5QXJKMF \
  | 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: b764576ff6c0b263e08b77dbd85d2a615a9e1d6f6998cfa89db077e18652cb48

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d631dbed6fcf7a867e54b23633cc772b408ce894c600bfe35f52256e44af0804",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2018-08-29T02:53:51Z",
    "title_canon_sha256": "ad5075c1bedc74a0e25371547f431d22e9cb59308b0d0c0274470fa940cd2acb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1808.09615",
    "kind": "arxiv",
    "version": 1
  }
}