Pith Number

pith:7J2BBVXA

pith:1996:7J2BBVXAAURV2MMHL2QI7O7ZIJ

not attested not anchored not stored refs pending

Hodge theory in the Sobolev topology for the de Rham complex

Luigi Fontana, Marco M. Peloso, Steven G. Krantz

arxiv:math/9601208 v1 · 1996-01-22 · 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{7J2BBVXAAURV2MMHL2QI7O7ZIJ}

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	2026-05-18T01:05:47.906214Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fa7410d6e005235d31875ea08fbbf9424bc0501e563959be855a64e43eb8da00

Aliases

arxiv: math/9601208 · arxiv_version: math/9601208v1 · doi: 10.48550/arxiv.math/9601208 · pith_short_12: 7J2BBVXAAURV · pith_short_16: 7J2BBVXAAURV2MMH · pith_short_8: 7J2BBVXA

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/7J2BBVXAAURV2MMHL2QI7O7ZIJ \
  | 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: fa7410d6e005235d31875ea08fbbf9424bc0501e563959be855a64e43eb8da00

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c05b817e7319ccf75270fd7fa06a4ed1c724e9289ef11528c2b48c7063d2dcd0",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.DG",
    "submitted_at": "1996-01-22T00:00:00Z",
    "title_canon_sha256": "86d25f3e3e07f805b935e7bb91625b40d58d4a42b85ea02fc5a0304557b3f08c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9601208",
    "kind": "arxiv",
    "version": 1
  }
}