Pith Number

pith:ZYD4WPPA

pith:2013:ZYD4WPPAQ76XNA63TNOZCTIYMN

not attested not anchored not stored refs pending

Lower semicontinuity of weak supersolutions to the porous medium equation

Benny Avelin, Teemu Lukkari

arxiv:1312.2820 v1 · 2013-12-10 · 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{ZYD4WPPAQ76XNA63TNOZCTIYMN}

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	2026-05-18T03:05:08.341295Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ce07cb3de087fd7683db9b5d914d18634f4d829b50c399396817bf0c136f1992

Aliases

arxiv: 1312.2820 · arxiv_version: 1312.2820v1 · doi: 10.48550/arxiv.1312.2820 · pith_short_12: ZYD4WPPAQ76X · pith_short_16: ZYD4WPPAQ76XNA63 · pith_short_8: ZYD4WPPA

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/ZYD4WPPAQ76XNA63TNOZCTIYMN \
  | 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: ce07cb3de087fd7683db9b5d914d18634f4d829b50c399396817bf0c136f1992

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "12f094d419fc2e6cfebad6c29b1152abc370f8c4fd3cb62f522953c908e1bcbf",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-12-10T14:54:59Z",
    "title_canon_sha256": "a422189a8707508d8279fb12908c22691c73f83e0d4946b2b4839f6b5c8479d8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.2820",
    "kind": "arxiv",
    "version": 1
  }
}