Pith Number

pith:MHHD7T6B

pith:2012:MHHD7T6BVXBNANPPG5ET3QNOLH

not attested not anchored not stored refs pending

The almost sure limits of the minimal position and the additive martingale in a branching random walk

Yueyun Hu (LAGA)

arxiv:1211.5309 v2 · 2012-11-22 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MHHD7T6BVXBNANPPG5ET3QNOLH}

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	2026-05-18T01:37:38.351894Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

61ce3fcfc1adc2d035ef37493dc1ae59d87d8cc023deff3be8f872c38e7e63ed

Aliases

arxiv: 1211.5309 · arxiv_version: 1211.5309v2 · doi: 10.48550/arxiv.1211.5309 · pith_short_12: MHHD7T6BVXBN · pith_short_16: MHHD7T6BVXBNANPP · pith_short_8: MHHD7T6B

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/MHHD7T6BVXBNANPPG5ET3QNOLH \
  | 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: 61ce3fcfc1adc2d035ef37493dc1ae59d87d8cc023deff3be8f872c38e7e63ed

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ba2ca9da86e77f2675b3b9f15b91eace9ca953362fed7cd5f57e68d5e1b9f7d4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-11-22T15:23:26Z",
    "title_canon_sha256": "f5f0f606a703bda8e8e4e3ba02cee239686d4426114d689a4db3af38ed7cdd84"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.5309",
    "kind": "arxiv",
    "version": 2
  }
}