Pith Number

pith:3UJZTPMH

pith:2021:3UJZTPMHDX3KX27ZBDWEEWYSDD

not attested not anchored not stored refs pending

Sobolev improving for averages over curves in $\mathbf{R^4}$

Andreas Seeger, David Beltran, Jonathan Hickman, Shaoming Guo

arxiv:2102.08806 v2 · 2021-02-17 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3UJZTPMHDX3KX27ZBDWEEWYSDD}

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	2026-07-05T03:24:56.118783Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dd1399bd871df6abebf908ec425b1218fc28021149283ccb9f8cd577203695a0

Aliases

arxiv: 2102.08806 · arxiv_version: 2102.08806v2 · doi: 10.48550/arxiv.2102.08806 · pith_short_12: 3UJZTPMHDX3K · pith_short_16: 3UJZTPMHDX3KX27Z · pith_short_8: 3UJZTPMH

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/3UJZTPMHDX3KX27ZBDWEEWYSDD \
  | 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: dd1399bd871df6abebf908ec425b1218fc28021149283ccb9f8cd577203695a0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f12c5608c368e872b73801fff57647fc86fb99145695fa2370cd3bbbe3a49cbd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2021-02-17T15:08:27Z",
    "title_canon_sha256": "3c7bb5443b01f4d5eb1a1a34d67b59a8ff49dcc013ab4d2ea26f9d74f09fbfeb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2102.08806",
    "kind": "arxiv",
    "version": 2
  }
}