{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:3SFMF24Z6FKOAEGOYD5YAQQATT","short_pith_number":"pith:3SFMF24Z","canonical_record":{"source":{"id":"1605.05191","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-05-17T14:40:13Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"3a4da0374b6609ab434901695a8c70abe90bf0e28bd43d37906bbcb8677500fa","abstract_canon_sha256":"0d63523568e182b117ad69c9587884d99e4e658b4142f300941589a43e6c917f"},"schema_version":"1.0"},"canonical_sha256":"dc8ac2eb99f154e010cec0fb8042009cd955bb2f7a9d805258296c6fd43ad4dc","source":{"kind":"arxiv","id":"1605.05191","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.05191","created_at":"2026-05-18T01:14:37Z"},{"alias_kind":"arxiv_version","alias_value":"1605.05191v1","created_at":"2026-05-18T01:14:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.05191","created_at":"2026-05-18T01:14:37Z"},{"alias_kind":"pith_short_12","alias_value":"3SFMF24Z6FKO","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"3SFMF24Z6FKOAEGO","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"3SFMF24Z","created_at":"2026-05-18T12:29:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:3SFMF24Z6FKOAEGOYD5YAQQATT","target":"record","payload":{"canonical_record":{"source":{"id":"1605.05191","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-05-17T14:40:13Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"3a4da0374b6609ab434901695a8c70abe90bf0e28bd43d37906bbcb8677500fa","abstract_canon_sha256":"0d63523568e182b117ad69c9587884d99e4e658b4142f300941589a43e6c917f"},"schema_version":"1.0"},"canonical_sha256":"dc8ac2eb99f154e010cec0fb8042009cd955bb2f7a9d805258296c6fd43ad4dc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:14:37.142634Z","signature_b64":"E+Pux2Qvh2QTJ617dFD3jzGQdtTl0MvnuLw/4G1gFCIFl0273F67s+yryLTs3tjDvxfq56wo1pI5WKDA4mNDAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dc8ac2eb99f154e010cec0fb8042009cd955bb2f7a9d805258296c6fd43ad4dc","last_reissued_at":"2026-05-18T01:14:37.141863Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:14:37.141863Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.05191","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:14:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GDrkessZRbh2xmwNbAjZB4cra9Fqh5JwA7wdHoAtWQvqP0HtPbEtJ9mcXJf0qBI7FEZGwarsT51V4qQ7nuw5Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T20:30:18.807330Z"},"content_sha256":"1d32365a294ec1fad1747ebd912a03e72422705eb1fe0abd1b1619fb6928c6b5","schema_version":"1.0","event_id":"sha256:1d32365a294ec1fad1747ebd912a03e72422705eb1fe0abd1b1619fb6928c6b5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:3SFMF24Z6FKOAEGOYD5YAQQATT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Graph limits of random graphs from a subset of connected $k$-trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Benedikt Stufler, Emma Yu Jin, Michael Drmota","submitted_at":"2016-05-17T14:40:13Z","abstract_excerpt":"For any set $\\Omega$ of non-negative integers such that $\\{0,1\\}\\subseteq \\Omega$ and $\\{0,1\\}\\ne \\Omega$, we consider a random $\\Omega$-$k$-tree ${\\sf G}_{n,k}$ that is uniformly selected from all connected $k$-trees of $(n+k)$ vertices where the number of $(k+1)$-cliques that contain any fixed $k$-clique belongs to $\\Omega$. We prove that ${\\sf G}_{n,k}$, scaled by $(kH_{k}\\sigma_{\\Omega})/(2\\sqrt{n})$ where $H_{k}$ is the $k$-th Harmonic number and $\\sigma_{\\Omega}>0$, converges to the Continuum Random Tree $\\mathcal{T}_{{\\sf e}}$. Furthermore, we prove the local convergence of the rooted r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.05191","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:14:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/jpv+Hho9cRc+7NlwRy6Hd+nhQZn4d1Ivm9BwgPGAVQiackPZvxXsXN6TGuRNox5iCKHj7P1bPH6JmwW6yzRAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T20:30:18.807674Z"},"content_sha256":"5935ac3243d63bf5cc5b8432bc06f05e46fe0b96eb2167376cb10dd42ee46954","schema_version":"1.0","event_id":"sha256:5935ac3243d63bf5cc5b8432bc06f05e46fe0b96eb2167376cb10dd42ee46954"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3SFMF24Z6FKOAEGOYD5YAQQATT/bundle.json","state_url":"https://pith.science/pith/3SFMF24Z6FKOAEGOYD5YAQQATT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3SFMF24Z6FKOAEGOYD5YAQQATT/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-21T20:30:18Z","links":{"resolver":"https://pith.science/pith/3SFMF24Z6FKOAEGOYD5YAQQATT","bundle":"https://pith.science/pith/3SFMF24Z6FKOAEGOYD5YAQQATT/bundle.json","state":"https://pith.science/pith/3SFMF24Z6FKOAEGOYD5YAQQATT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3SFMF24Z6FKOAEGOYD5YAQQATT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:3SFMF24Z6FKOAEGOYD5YAQQATT","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"0d63523568e182b117ad69c9587884d99e4e658b4142f300941589a43e6c917f","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-05-17T14:40:13Z","title_canon_sha256":"3a4da0374b6609ab434901695a8c70abe90bf0e28bd43d37906bbcb8677500fa"},"schema_version":"1.0","source":{"id":"1605.05191","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.05191","created_at":"2026-05-18T01:14:37Z"},{"alias_kind":"arxiv_version","alias_value":"1605.05191v1","created_at":"2026-05-18T01:14:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.05191","created_at":"2026-05-18T01:14:37Z"},{"alias_kind":"pith_short_12","alias_value":"3SFMF24Z6FKO","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"3SFMF24Z6FKOAEGO","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"3SFMF24Z","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:5935ac3243d63bf5cc5b8432bc06f05e46fe0b96eb2167376cb10dd42ee46954","target":"graph","created_at":"2026-05-18T01:14:37Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"For any set $\\Omega$ of non-negative integers such that $\\{0,1\\}\\subseteq \\Omega$ and $\\{0,1\\}\\ne \\Omega$, we consider a random $\\Omega$-$k$-tree ${\\sf G}_{n,k}$ that is uniformly selected from all connected $k$-trees of $(n+k)$ vertices where the number of $(k+1)$-cliques that contain any fixed $k$-clique belongs to $\\Omega$. We prove that ${\\sf G}_{n,k}$, scaled by $(kH_{k}\\sigma_{\\Omega})/(2\\sqrt{n})$ where $H_{k}$ is the $k$-th Harmonic number and $\\sigma_{\\Omega}>0$, converges to the Continuum Random Tree $\\mathcal{T}_{{\\sf e}}$. Furthermore, we prove the local convergence of the rooted r","authors_text":"Benedikt Stufler, Emma Yu Jin, Michael Drmota","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-05-17T14:40:13Z","title":"Graph limits of random graphs from a subset of connected $k$-trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.05191","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:1d32365a294ec1fad1747ebd912a03e72422705eb1fe0abd1b1619fb6928c6b5","target":"record","created_at":"2026-05-18T01:14:37Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"0d63523568e182b117ad69c9587884d99e4e658b4142f300941589a43e6c917f","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-05-17T14:40:13Z","title_canon_sha256":"3a4da0374b6609ab434901695a8c70abe90bf0e28bd43d37906bbcb8677500fa"},"schema_version":"1.0","source":{"id":"1605.05191","kind":"arxiv","version":1}},"canonical_sha256":"dc8ac2eb99f154e010cec0fb8042009cd955bb2f7a9d805258296c6fd43ad4dc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dc8ac2eb99f154e010cec0fb8042009cd955bb2f7a9d805258296c6fd43ad4dc","first_computed_at":"2026-05-18T01:14:37.141863Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:14:37.141863Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E+Pux2Qvh2QTJ617dFD3jzGQdtTl0MvnuLw/4G1gFCIFl0273F67s+yryLTs3tjDvxfq56wo1pI5WKDA4mNDAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:14:37.142634Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.05191","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1d32365a294ec1fad1747ebd912a03e72422705eb1fe0abd1b1619fb6928c6b5","sha256:5935ac3243d63bf5cc5b8432bc06f05e46fe0b96eb2167376cb10dd42ee46954"],"state_sha256":"09b54882b158bf118040045ea0856d77be00fae91f5e9941af3aeb6782ed6ed0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J/ZmDz9i5bLlp6AhPHDjNjKQg159TlQ+liGr5e45+aBNnKUgi4yWpNm/YDBRhOHdxc5yRV8pZ5asMR3+X5QACg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T20:30:18.809694Z","bundle_sha256":"a343a14ee62eb32e43db74212fa3e1355bcfd6c909d315aa3f95d1fa36b46c2f"}}