Here's another one: https://patents.google.com/patent/US20170133938 He claims the startup power is just 100nW. For contrast, TI says their BQ255xx chip requires 15 uW. i.e. an entire order of magnitude more. Sounds too good to be true, doesn't it? Which leads me to wonder: just how well are patents vetted before they're granted? Might it still be granted even if the author never made a a circuit that performed anywhere near as well as the patent claims? Is anyone even checking? By the way, on a different topic, this might interest you: https://www.mouser.com/ProductDetail/426-DFR0579 It's a $12.90, 30mmx30mm, fully assembled breakout for the SPV1050, configured as a boost converter.

@Mishka Ah yes, that is true. In this case though I went out of my way to keep the PCB dimensions as small as possible so that someone could have it made at OSH-PARK for super cheap--just $0.30 per board. If I ever figure out how to post a complete set of KiCAD files, then I guess maybe then everyone can modify it to suit their circumstances. Until then, it will be hard to have one's cake and eat it too.

If you wish, you may substitute S-1313 ( http://datasheet.sii-ic.com/en/voltage_regulator/S1313_E.pdf) for the MAX8887EZK27 LDO

What is the max ampere capacity of 3.3V battery it can charge ? Is there any upper limit like 1000mAh or 3300mAh like that ?

Right you are. Live and learn (even at 81), and I even learned a new word -'vias.' Thanks.