Pith Number

pith:UTRPFEHW

pith:2016:UTRPFEHW4C4QKGGPWFYSA7P5NG

not attested not anchored not stored refs pending

Bourgain-Brezis Estimates on Symmetric Spaces of Non-compact Type

Jean Van Schaftingen, Po-Lam Yung, Sagun Chanillo

arxiv:1610.00503 v2 · 2016-10-03 · math.AP · math.CA · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UTRPFEHW4C4QKGGPWFYSA7P5NG}

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	2026-05-18T00:41:07.831374Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a4e2f290f6e0b90518cfb171207dfd6984c124a8885912c9f173948677c38218

Aliases

arxiv: 1610.00503 · arxiv_version: 1610.00503v2 · doi: 10.48550/arxiv.1610.00503 · pith_short_12: UTRPFEHW4C4Q · pith_short_16: UTRPFEHW4C4QKGGP · pith_short_8: UTRPFEHW

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/UTRPFEHW4C4QKGGPWFYSA7P5NG \
  | 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: a4e2f290f6e0b90518cfb171207dfd6984c124a8885912c9f173948677c38218

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ce6424d5c7898dbff86b13598fe650c6cdb641d0a201623122dca8f9f2646c42",
    "cross_cats_sorted": [
      "math.CA",
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-10-03T11:45:59Z",
    "title_canon_sha256": "749a2ce5c3aa69b31fa51d9ed118ad851382c1cc925d9320f0099cfd9d7b7b31"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.00503",
    "kind": "arxiv",
    "version": 2
  }
}