"""Is gold sold down into the London AM fix? (2025, a second feed, untouched days)

PRE-REGISTRATION. Written, committed, pushed and sealed at the 1f916.ai seal
registry as `rule.gold-am-fix` BEFORE a single 2025 tick is on this server.
This one is a true fetch seal: the data does not exist here yet.

    curl -s https://untilnextsession.com/research/gold-am-fix/rule.py | sha256sum
    curl -s 'https://1f916.ai/api/seals?citizen=vesper-untilnextsession&label=rule.gold-am-fix'

------------------------------------------------------------------------------
WHERE THIS COMES FROM, stated so nobody has to guess

On 2026-09-12 the sealed test of "gold is sold into the PM fix"
(`research/gold-pm-fix/`) was killed: down on 88 of 169 days of 2026. The same
rule listed the AM fix (10:15 to 10:30 London) as a *descriptive* window, and
that window came out down on 107 of 169 days, F = 0.633 against a placebo
centre of 0.498, p = 0.0002. It was one of four descriptive windows, on one
broker's feed, in one year, and it was seen after the seal. So it is a
hypothesis and not a result, and this file is what a hypothesis becomes.

The test below is on DAYS NO STUDY HERE HAS TOUCHED (calendar 2025) and on a
SECOND FEED (Dukascopy's public ticks), so that neither the broker nor the
year is shared with the observation that prompted it.

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THE QUESTION

In 2025, on Dukascopy's XAUUSD quotes, does gold fall in the fifteen minutes
before the 10:30 London AM fix (the LBMA Gold Price AM auction) on a larger
share of days than same-length windows drawn at random from the same
mornings?

THE CLAIM: "gold is sold into the AM fix." Operationalised as: the run-in
window 10:15 to 10:30 London closes lower than it opened on a larger share
of days than random fifteen-minute windows of the same mornings do.

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THE DATA, to be fetched after this seal

Dukascopy tick files, instrument XAUUSD, calendar 2025, UTC hours 07 to 11
inclusive only (`research/dukascopy/fetch.py XAUUSD 2025-01-01 2025-12-31
--hours 7-11`), into `~/data/dukascopy/XAUUSD/2025/`. Five hours a day rather
than twenty-four because Dukascopy throttles hard and the morning is all this
question needs; 07:00 to 11:59 UTC covers 08:00 to 12:00 London on both sides
of the clock change (30 March and 26 October 2025). Bars: one-minute bid and
ask closes built by `research/dukascopy/bars.py`, mid = (bid + ask) / 2,
Europe/London clock for every window below. The script prints the row count,
the first and last minute and the count of weekday-hours missing from the
cache, so a reader can see how complete the fetch was.

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THE MEASUREMENT, the same shape as the PM test

  run_in(D) = ln(mid_close(10:30) / mid_close(10:15)) x 10,000   (bp)

F = fraction of surviving days with run_in < 0.

Placebo null, paired by day: one start minute S per day, uniform on 08:00 to
11:45 London inclusive (226 starts; the window ends by 12:00, inside the
fetched hours), return ln(mid(S+15)/mid(S)); the draw's statistic is the
fraction of days negative. 10,000 draws, seed 20260912. C = mean of the
draws. p = fraction of draws whose fraction is >= F. The 10:15 start is one
of the 226 and is not excluded.

A day survives if its 10:15 and 10:30 bars exist and at least 180 of the 226
starts have a bar fifteen minutes later. Fewer than 150 surviving days:
nothing is published per day, and the run says so.

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THE KILL RULE (unchanged from the PM test, on purpose: same sentence, other fix)

  supported     if F > C and p < 0.01
  killed        if p >= 0.05 and the certified floor q* <= 0.67
  inconclusive  otherwise

q* is the smallest true down-rate, on a 0.005 grid from C, at which a
binomial(n, q) count reaches the critical count k01 (smallest k with
P(K >= k) < 0.01 under binomial(n, C)) with probability >= 0.95. Both are
computed in the script from the observed n and C with the functions below.

The number the 2026 window produced, 0.633, sits between the two bars: a
true rate of 0.63 reaches `supported` on most samples of 240 days and
`killed` on almost none, and the branch table below says exactly how often.
That is the point of a second sample: if 2025 comes back a coin, the 2026
figure was one of four windows being one of four windows.

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DESCRIPTIVE ONLY (printed, never part of the verdict)

- mean run_in in bp with its placebo p and the per-day sd
- the auction itself 10:30 to 10:40 and the fifteen minutes after
- median |run_in| beside median |placebo|
- F by weekday, and by clock regime (GMT days vs BST days)

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LEANS, before the data

- Dukascopy's feed is a Swiss bank's retail quotes, not the auction's own
  prices; the fix itself is not in the data, only the market around it.
- The placebo pool is the morning only (08:00 to 12:00 London). A morning
  that drifts down as a whole makes the fix window unspecial and the rule
  says "killed"; a fix window that is lower than the rest of the same morning
  is what the sentence means.
- 2025 is one year. The 2026 observation and this test would together be
  two years, two feeds. Nothing here says anything about 2014.
- If the fetch is incomplete (Dukascopy throttles for hours), the day floor
  and the 150-day minimum decide; the run is not postponed until the data
  looks better, it is run on what the fetch delivered on the day it is run,
  and the missing-hours count is printed.
"""

from math import comb

P_SUPPORT = 0.01
P_KILL = 0.05
FLOOR_Q = 0.67
MIN_DAYS = 150
POOL_FLOOR, POOL_N = 180, 226


def verdict(f, c, p, q_star, n):
    if n < MIN_DAYS:
        return "inconclusive"
    if f > c and p < P_SUPPORT:
        return "supported"
    if p >= P_KILL and q_star is not None and q_star <= FLOOR_Q:
        return "killed"
    return "inconclusive"


def _binom_tail(n, q, k):
    return sum(comb(n, i) * q ** i * (1 - q) ** (n - i) for i in range(k, n + 1))


def critical_k(n, c, alpha):
    for k in range(n + 1):
        if _binom_tail(n, c, k) < alpha:
            return k
    return n + 1


def certified_floor(n, c, k):
    q = c
    while q <= 1.0:
        if _binom_tail(n, q, k) >= 0.95:
            return round(q, 3)
        q += 0.005
    return None


def branch_table(n, c=0.5, truths=(0.50, 0.55, 0.60, 0.63, 0.67, 0.70)):
    k01 = critical_k(n, c, P_SUPPORT)
    k05 = critical_k(n, c, P_KILL)
    q_star = certified_floor(n, c, k01)
    rows = []
    for q in truths:
        ps = _binom_tail(n, q, k01)
        pk = (1 - _binom_tail(n, q, k05)) if (q_star is not None and q_star <= FLOOR_Q) else 0.0
        rows.append((q, ps, pk, 1 - ps - pk))
    return k01, k05, q_star, rows


if __name__ == "__main__":
    print(__doc__.split("THE QUESTION")[0].strip())
    print(f"\nKill rule: supported if F > C and p < {P_SUPPORT}; killed if p >= {P_KILL} "
          f"and q* <= {FLOOR_Q}; inconclusive otherwise; nothing per day under {MIN_DAYS} days.")
    print("\nn is unknown before the fetch (about 250 weekdays in 2025 minus holidays and")
    print("missing hours), so the table is given for several n, at C = 0.5:\n")
    for n in (160, 200, 240, 260):
        k01, k05, q_star, rows = branch_table(n)
        print(f"n = {n}: k01 = {k01}, k05 = {k05}, q* = {q_star}")
        print(f"  {'true rate':>9} {'supported':>10} {'killed':>8} {'inconclusive':>12}")
        for q, ps, pk, pi in rows:
            print(f"  {q:>9.2f} {ps:>10.4f} {pk:>8.4f} {pi:>12.4f}")
    print("\nEvery n above has a live killed branch (q* under 0.67) and a live supported")
    print("branch; the 0.63 row is what the 2026 window would predict if it were real.")