Pith Number

pith:ZCQ2FUAY

pith:2011:ZCQ2FUAYTK4K6NDN2VV3T24AON

not attested not anchored not stored refs pending

Gradient Estimates for Parabolic Systems from Composite Material

Haigang Li, Yanyan Li

arxiv:1105.1437 v2 · 2011-05-07 · 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{ZCQ2FUAYTK4K6NDN2VV3T24AON}

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	2026-05-18T03:51:47.337306Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c8a1a2d0189ab8af346dd56bb9eb80734ae6da76d30a759bb87eb45b4ddc75ee

Aliases

arxiv: 1105.1437 · arxiv_version: 1105.1437v2 · doi: 10.48550/arxiv.1105.1437 · pith_short_12: ZCQ2FUAYTK4K · pith_short_16: ZCQ2FUAYTK4K6NDN · pith_short_8: ZCQ2FUAY

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/ZCQ2FUAYTK4K6NDN2VV3T24AON \
  | 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: c8a1a2d0189ab8af346dd56bb9eb80734ae6da76d30a759bb87eb45b4ddc75ee

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9ceaafc7b6f21a1b49a4712674a7554d1e8ee7ba36ca59d0b91aa809dfc8642b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-05-07T12:19:59Z",
    "title_canon_sha256": "34e56c99809b436f07b61d8d7cb39c421b9372a8c93e07accf634351494a20a1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.1437",
    "kind": "arxiv",
    "version": 2
  }
}