    Whisper theoretical model. Attempts to encode characteristics of it.

    Goals:
    1. Ensure network scales by being user or usage bound, as opposed to bandwidth growing in proportion to network size.
    2. Staying with in a reasonable bandwidth limit for limited data plans.
    3. Do the above without materially impacting existing nodes.

    Case 1. Only receiving messages meant for you [naive case]

    Assumptions:
    - A1. Envelope size (static): 1024kb
    - A2. Envelopes / message (static): 10
    - A3. Received messages / day (static): 100
    - A4. Only receiving messages meant for you.

    For 100 users, receiving bandwidth is 1000.0KB/day
    For 10k users, receiving bandwidth is 1000.0KB/day
    For  1m users, receiving bandwidth is 1000.0KB/day

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    Case 2. Receiving messages for everyone [naive case]

    Assumptions:
    - A1. Envelope size (static): 1024kb
    - A2. Envelopes / message (static): 10
    - A3. Received messages / day (static): 100
    - A5. Received messages for everyone.

    For 100 users, receiving bandwidth is   97.7MB/day
    For 10k users, receiving bandwidth is    9.5GB/day
    For  1m users, receiving bandwidth is  953.7GB/day

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    Case 3. All private messages go over one discovery topic

    Assumptions:
    - A1. Envelope size (static): 1024kb
    - A2. Envelopes / message (static): 10
    - A3. Received messages / day (static): 100
    - A6. Proportion of private messages (static): 0.5
    - A7. Public messages only received by relevant recipients (static).
    - A8. All private messages are received by everyone (same topic) (static).

    For 100 users, receiving bandwidth is   49.3MB/day
    For 10k users, receiving bandwidth is    4.8GB/day
    For  1m users, receiving bandwidth is  476.8GB/day

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    Case 4. All private messages are partitioned into shards [naive case]

    Assumptions:
    - A1. Envelope size (static): 1024kb
    - A2. Envelopes / message (static): 10
    - A3. Received messages / day (static): 100
    - A6. Proportion of private messages (static): 0.5
    - A7. Public messages only received by relevant recipients (static).
    - A9. Private messages are partitioned evenly across partition shards (static), n=5000

    For 100 users, receiving bandwidth is 1000.0KB/day
    For 10k users, receiving bandwidth is    1.5MB/day
    For  1m users, receiving bandwidth is   98.1MB/day

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    Case 5. Case 4 + All messages are passed through bloom filter with false positive rate

    Assumptions:
    - A1. Envelope size (static): 1024kb
    - A2. Envelopes / message (static): 10
    - A3. Received messages / day (static): 100
    - A6. Proportion of private messages (static): 0.5
    - A7. Public messages only received by relevant recipients (static).
    - A9. Private messages are partitioned evenly across partition shards (static), n=5000
    - A10. Bloom filter size (m) (static): 512
    - A11. Bloom filter hash functions (k) (static): 3
    - A12. Bloom filter elements, i.e. topics, (n) (static): 100
    - A13. Bloom filter assuming optimal k choice (sensitive to m, n).
    - A14. Bloom filter false positive proportion of full traffic, p=0.1

    For 100 users, receiving bandwidth is   10.7MB/day
    For 10k users, receiving bandwidth is  978.0MB/day
    For  1m users, receiving bandwidth is   95.5GB/day

    NOTE: Traffic extremely sensitive to bloom false positives
    This completely dominates network traffic at scale.
    With p=1% we get 10k users ~100MB/day and 1m users ~10gb/day)
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    Case 6. Case 5 + Benign duplicate receives

    Assumptions:
    - A1. Envelope size (static): 1024kb
    - A2. Envelopes / message (static): 10
    - A3. Received messages / day (static): 100
    - A6. Proportion of private messages (static): 0.5
    - A7. Public messages only received by relevant recipients (static).
    - A9. Private messages are partitioned evenly across partition shards (static), n=5000
    - A10. Bloom filter size (m) (static): 512
    - A11. Bloom filter hash functions (k) (static): 3
    - A12. Bloom filter elements, i.e. topics, (n) (static): 100
    - A13. Bloom filter assuming optimal k choice (sensitive to m, n).
    - A14. Bloom filter false positive proportion of full traffic, p=0.1
    - A15. Benign duplicate receives factor (static): 2
    - A16. No bad envelopes, bad PoW, expired, etc (static).

    For 100 users, receiving bandwidth is   21.5MB/day
    For 10k users, receiving bandwidth is    1.9GB/day
    For  1m users, receiving bandwidth is  190.9GB/day

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    Case 7. Case 6 + Mailserver case under good conditions with smaller bloom false positive and mostly offline

    Assumptions:
    - A1. Envelope size (static): 1024kb
    - A2. Envelopes / message (static): 10
    - A3. Received messages / day (static): 100
    - A6. Proportion of private messages (static): 0.5
    - A7. Public messages only received by relevant recipients (static).
    - A9. Private messages are partitioned evenly across partition shards (static), n=5000
    - A10. Bloom filter size (m) (static): 512
    - A11. Bloom filter hash functions (k) (static): 3
    - A12. Bloom filter elements, i.e. topics, (n) (static): 100
    - A13. Bloom filter assuming optimal k choice (sensitive to m, n).
    - A14. Bloom filter false positive proportion of full traffic, p=0.1
    - A15. Benign duplicate receives factor (static): 2
    - A16. No bad envelopes, bad PoW, expired, etc (static).
    - A17. User is offline p% of the time (static) p=0.9
    - A18. No bad request, duplicate messages for mailservers, and overlap/retires are perfect (static).
    - A19. Mailserver requests can change false positive rate to be p=0.01

    For 100 users, receiving bandwidth is    3.9MB/day
    For 10k users, receiving bandwidth is  284.8MB/day
    For  1m users, receiving bandwidth is   27.8GB/day

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    Case 8. Waka mode - no metadata protection with bloom filter and one node connected; still static shard

    Next step up is to either only use contact code, or shard more aggressively.
    Note that this requires change of other nodes behavior, not just local node.

    Assumptions:
    - A1. Envelope size (static): 1024kb
    - A2. Envelopes / message (static): 10
    - A3. Received messages / day (static): 100
    - A6. Proportion of private messages (static): 0.5
    - A7. Public messages only received by relevant recipients (static).
    - A9. Private messages are partitioned evenly across partition shards (static), n=5000

    For 100 users, receiving bandwidth is 1000.0KB/day
    For 10k users, receiving bandwidth is    1.5MB/day
    For  1m users, receiving bandwidth is   98.1MB/day

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